TOHOKU UNIVERSITY Researchers

Details of the Researcher

Home

日本語 English

Akihiro Munemasa

Section

Graduate School of Information Sciences

Job title

Professor

Degree

Ｐｈ．Ｄ（オハイオ州立大学）

researchmap

https://researchmap.jp/munemasa

J-GLOBAL ID

200901003156143100

Research History 1

2003/04 - Present

Tohoku University　Graduate School of Information Sciences　Professor

Education 1

The Ohio State University　Department of Mathematics

1985/06 - 1989/06

Committee Memberships 4

Mathematical Society of Japan　Algebra Section Committee Member

2021/04 - Present
Algebraic Combinatorics　Editors-in-Chief

2017/07 - Present
Mathematical Society of Japan　Algebra Prize Comittee

2018/04 - 2022/03
Journal of Algebraic Combinatorics　Editors-in-Chief

2000/04 - 2017/07

Professional Memberships 2

American Mathematical Society
Mathematical Society of Japan

Research Interests 3

lattice
combinatorics
permutation group

Research Areas 3

Natural sciences / Applied mathematics and statistics /
Natural sciences / Basic mathematics /
Natural sciences / Algebra /

Papers 85

Sets of equiangular lines in dimension 18 constructed from A9 ⊕ A9 ⊕ A1

Yen-chi Roger Lin, Akihiro Munemasa, Tetsuji Taniguchi, Kiyoto Yoshino

Linear Algebra and its Applications　2025/11

DOI： 10.1016/j.laa.2025.06.015 　
A note on t-designs in isodual codes Peer-reviewed

Madoka Awada, Tsuyoshi Miezaki, Akihiro Munemasa, Hiroyuki Nakasora

Finite Fields and Their Applications　95　102366-102366　2024/03
Publisher: Elsevier BV
DOI： 10.1016/j.ffa.2024.102366 　

ISSN： 1071-5797
Jacobi polynomials and harmonic weight enumerators of the first-order Reed–Muller codes and the extended Hamming codes Peer-reviewed

Tsuyoshi Miezaki, Akihiro Munemasa

Designs, Codes and Cryptography　92　(4)　1041-1049　2023/11/16
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s10623-023-01327-0 　

ISSN： 0925-1022

eISSN： 1573-7586
Classification of extremal type II $$\mathbb {Z}_4$$-codes of length 24 Peer-reviewed

Akihiro Munemasa, Rowena Alma L. Betty

Designs, Codes and Cryptography　92　(3)　771-785　2023/09/10
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s10623-023-01293-7 　

ISSN： 0925-1022

eISSN： 1573-7586
Maximal digraphs whose Hermitian spectral radius is at most 2 Peer-reviewed

Alexander L. Gavrilyuk, Akihiro Munemasa

Linear Algebra and its Applications　658　331-349　2023/02
Publisher: Elsevier BV
DOI： 10.1016/j.laa.2022.11.007 　

ISSN： 0024-3795
Extended double covers of non-symmetric association schemes of class $2$ Peer-reviewed

Takuya Ikuta, Akihiro Munemasa

2023
Quasi-symmetric 2-(41, 9, 9) designs and doubly even self-dual codes of length 40 Peer-reviewed

Akihiro Munemasa, Vladimir D. Tonchev

Applicable Algebra in Engineering, Communication and Computing　33　(6)　855-866　2022/02/10
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00200-022-00543-w 　

ISSN： 0938-1279

eISSN： 1432-0622
Maximality of Seidel matrices and switching roots of graphs Peer-reviewed

Meng-Yue Cao, Jack H. Koolen, Akihiro Munemasa, Kiyoto Yoshino

Graphs and Combinatorics　37　(5)　1491-1507　2021/07/03
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00373-021-02359-w 　

ISSN： 0911-0119

eISSN： 1435-5914
Signed analogue of line graphs and their smallest eigenvalues Peer-reviewed

Alexander L. Gavrilyuk, Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

Journal of Graph Theory　98　(2)　309-325　2021/06/08
Publisher: Wiley
DOI： 10.1002/jgt.22699 　

ISSN： 0364-9024

eISSN： 1097-0118
A note on Assmus–Mattson type theorems Peer-reviewed

Tsuyoshi Miezaki, Akihiro Munemasa, Hiroyuki Nakasora

Designs, Codes and Cryptography　89　(5)　843-858　2021/02/23
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s10623-021-00848-w 　

ISSN： 0925-1022

eISSN： 1573-7586
Bordered Complex Hadamard Matrices and Strongly Regular Graphs Peer-reviewed

Takuya IKUTA, Akihiro MUNEMASA

Interdisciplinary Information Sciences　27　(1)　41-56　2021
Publisher: Graduate School of Information Sciences, Tohoku University
DOI： 10.4036/iis.2020.r.03 　

ISSN： 1340-9050

eISSN： 1347-6157
Ternary codes, biplanes, and the nonexistence of some quasisymmetric and quasi-3 designs Peer-reviewed

Akihiro Munemasa, Vladimir D. Tonchev

Journal of Combinatorial Designs　28　(10)　745-752　2020/10/01
Publisher: John Wiley and Sons Inc.
DOI： 10.1002/jcd.21740 　

ISSN： 1520-6610 1063-8539
Complex Hadamard Matrices Attached to a 3-Class Nonsymmetric Association Scheme Peer-reviewed

Takuya Ikuta, Akihiro Munemasa

Graphs and Combinatorics　35　(6)　1293-1304　2019/11/16
Publisher: Springer Science and Business Media {LLC}
DOI： 10.1007/s00373-019-02044-z 　
Bent Vectorial Functions, Codes and Designs

Cunsheng Ding, Akihiro Munemasa, Vladimir D. Tonchev

IEEE Transactions on Information Theory　65　(11)　7533-7541　2019/11
Publisher: Institute of Electrical and Electronics Engineers ({IEEE})
DOI： 10.1109/TIT.2019.2922401 　
Classification of Self-dual Codes of Length 20 over Z4 and Length at Most 18 over F2+uF2 Peer-reviewed

Rowena Alma L. Betty, Akihiro Munemasa

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)　11929　64-77　2019
Publisher: Springer
DOI： 10.1007/978-3-030-35199-1_4 　

ISSN： 1611-3349 0302-9743
Some restrictions on weight enumerators of singly even self-dual codes II Peer-reviewed

Masaaki Harada, Akihiro Munemasa

Interdiscip. Inform. Sci.　24　77-85　2018/06
Butson-Type complex Hadamard matrices and association schemes on Galois rings of characteristic 4 Peer-reviewed

Takuya Ikuta, Akihiro Munemasa

Special Matrices　6　(1)　1-10　2018/01/01
Publisher: De Gruyter Open Ltd
DOI： 10.1515/spma-2018-0001 　

ISSN： 2300-7451
Nonexistence of certain singly even self-dual codes with minimal shadow Peer-reviewed

Stefka Bouyuklieva, Masaaki Harada, Akihiro Munemasa

Electronic J. Combin.　25　P1.13　2018/01
On a Lower Bound for the Laplacian Eigenvalues of a Graph Peer-reviewed

Gary R. W. Greaves, Akihiro Munemasa, Anni Peng

GRAPHS AND COMBINATORICS　33　(6)　1509-1519　2017/11

DOI： 10.1007/s00373-017-1835-y 　

ISSN： 0911-0119

eISSN： 1435-5914
On s-extremal singly even self-dual [24 kappa+8,121 kappa+4, 4 kappa+2] codes Peer-reviewed

Masaaki Harada, Akihiro Munemasa

FINITE FIELDS AND THEIR APPLICATIONS　48　306-317　2017/11

DOI： 10.1016/j.ffa.2017.08.008 　

ISSN： 1071-5797

eISSN： 1090-2465
Self-dual codes and the non-existence of a quasi-symmetric 2-(37,9,8) design with intersection numbers 1 and 3 Peer-reviewed

Masaaki Harada, Akihiro Munemasa, Vladimir D. Tonchev

J. Combin. Designs　25　469-476　2017/08
Godsil-McKay switching and twisted Grassmann graphs Peer-reviewed

Akihiro Munemasa

DESIGNS CODES AND CRYPTOGRAPHY　84　(1-2)　173-179　2017/07

DOI： 10.1007/s10623-016-0244-1 　

ISSN： 0925-1022

eISSN： 1573-7586
On the classification of self-dual Zk-codes II Peer-reviewed

Masaaki Harada, Akihiro Munemasa

Interdiscip. Inform. Sci.　22　(1)　81-85　2016/11
Publisher: Graduate School of Information Sciences, Tohoku University
DOI： 10.4036/iis.2015.R.01 　

ISSN： 1347-6157

More details Close

In this short note, we report the classification of self-dual \mathbb{Z}_k-codes of length n for k ≤ 24 and n ≤ 9.
On the classification of self-dual [20,10,9] codes over GF(7) Peer-reviewed

Masaaki Harada, Akihiro Munemasa

FINITE FIELDS AND THEIR APPLICATIONS　42　(1)　57-66　2016/11

DOI： 10.1016/j.ffa.2016.07.004 　

ISSN： 1071-5797

eISSN： 1090-2465
Equiangular lines in Euclidean spaces Peer-reviewed

Gary Greaves, Jacobus H. Koolen, Akihiro Munemasa, Ferenc Szoellosi

JOURNAL OF COMBINATORIAL THEORY SERIES A　138　208-235　2016/02

DOI： 10.1016/j.jcta.2015.09.008 　

ISSN： 0097-3165

eISSN： 1096-0899
On the smallest eigenvalues of the line graphs of some trees Peer-reviewed

Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

LINEAR ALGEBRA AND ITS APPLICATIONS　466　501-511　2015/02

DOI： 10.1016/j.laa.2014.10.037 　

ISSN： 0024-3795

eISSN： 1873-1856
Edge-signed graphs with smallest eigenvalue greater than - 2 Peer-reviewed

Gary Greaves, Jack Koolen, Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

JOURNAL OF COMBINATORIAL THEORY SERIES B　110　90-111　2015/01

DOI： 10.1016/j.jctb.2014.07.006 　

ISSN： 0095-8956

eISSN： 1096-0902
Complex Hadamard Matrices contained in a Bose-Mesner algebra Peer-reviewed

Takuya Ikuta, Akihiro Munemasa

Special Matrices　3　(1)　91-110　2015/01/01
Publisher: De Gruyter Open Ltd
DOI： 10.1515/spma-2015-0009 　

ISSN： 2300-7451
Fat Hoffman graphs with smallest eigenvalue greater than-3 Peer-reviewed

Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

DISCRETE APPLIED MATHEMATICS　176　(SI)　78-88　2014/10

DOI： 10.1016/j.dam.2014.01.008 　

ISSN： 0166-218X

eISSN： 1872-6771
On fat Hoffman graphs with smallest eigenvalue at least-3 Peer-reviewed

Hye Jin Jang, Jack Koolen, Akihiro Munemasa, Tetsuji Taniguchi

ARS MATHEMATICA CONTEMPORANEA　7　(1)　105-121　2014

ISSN： 1855-3966

eISSN： 1855-3974
Fat Hoffman graphs with smallest eigenvalue at least-1-tau Peer-reviewed

Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

ARS MATHEMATICA CONTEMPORANEA　7　(1)　247-262　2014

ISSN： 1855-3966

eISSN： 1855-3974
Residue codes of extremal Type II Z(4)-codes and the moonshine vertex operator algebra Peer-reviewed

Masaaki Harada, Ching Hung Lam, Akihiro Munemasa

MATHEMATISCHE ZEITSCHRIFT　274　(1-2)　685-700　2013/06

DOI： 10.1007/s00209-012-1091-z 　

ISSN： 0025-5874
Upper bounds on cyclotomic numbers Peer-reviewed

Koichi Betsumiya, Mitsugu Hirasaka, Takao Komatsu, Akihiro Munemasa

Linear Algebra and Its Applications　438　(1)　111-120　2013/01/01

DOI： 10.1016/j.laa.2012.06.045 　

ISSN： 0024-3795
Spin models constructed from Hadamard matrices Peer-reviewed

Takuya Ikuta, Akihiro Munemasa

Journal of Applied Mathematics and Computing　40　(1-2)　231-248　2012/10

DOI： 10.1007/s12190-012-0547-y 　

ISSN： 1598-5865
Nomura algebras of nonsymmetric Hadamard models Peer-reviewed

Takuya Ikuta, Akihiro Munemasa

DESIGNS CODES AND CRYPTOGRAPHY　65　(1-2)　99-106　2012/10

DOI： 10.1007/s10623-012-9609-2 　

ISSN： 0925-1022
On triply even binary codes Peer-reviewed

Koichi Betsumiya, Akihiro Munemasa

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES　86　(1)　1-16　2012/08

DOI： 10.1112/jlms/jdr054 　

ISSN： 0024-6107
A complete classification of doubly even self-dual codes of length 40 Peer-reviewed

Koichi Betsumiya, Masaaki Harada, Akihiro Munemasa

ELECTRONIC JOURNAL OF COMBINATORICS　19　(3)　P18　2012/08

ISSN： 1077-8926
CLASSIFICATION OF SELF-DUAL CODES OF LENGTH 36 Peer-reviewed

Masaaki Harada, Akihiro Munemasa

ADVANCES IN MATHEMATICS OF COMMUNICATIONS　6　(2)　229-235　2012/05

DOI： 10.3934/amc.2012.6.229 　

ISSN： 1930-5346
The codes and the lattices of Hadamard matrices Peer-reviewed

Akihiro Munemasa, Hiroki Tamura

EUROPEAN JOURNAL OF COMBINATORICS　33　(4)　519-533　2012/05

DOI： 10.1016/j.ejc.2011.11.007 　

ISSN： 0195-6698
Steiner quadruple systems with point-regular abelian automorphism groups Peer-reviewed

Akihiro Munemasa, Masanori Sawa

Journal of Statistical Theory and Practice　6　(1)　97-128　2012/03/01

DOI： 10.1080/15598608.2012.647536 　

ISSN： 1559-8608 1559-8616
A note on super Catalan numbers Peer-reviewed

Evangelos Georgiadis, Akihiro Munemasa, Hajime Tanaka

Interdisciplinary Information Sciences　18　(1)　23-24　2012
Publisher: Tohoku University
DOI： 10.4036/iis.2012.23 　

ISSN： 1340-9050

More details Close

We show that the super Catalan numbers are special values of the Krawtchouk polynomials by deriving an expression for the super Catalan numbers in terms of a signed set.
On the classification of weighing matrices and self-orthogonal codes Peer-reviewed

Masaaki Harada, Akihiro Munemasa

JOURNAL OF COMBINATORIAL DESIGNS　20　(1)　40-57　2012/01

DOI： 10.1002/jcd.20295 　

ISSN： 1063-8539
Hamming graphs in Nomura algebras Peer-reviewed

Ada Chan, Akihiro Munemasa

LINEAR ALGEBRA AND ITS APPLICATIONS　435　(2)　330-341　2011/07

DOI： 10.1016/j.laa.2011.01.020 　

ISSN： 0024-3795

eISSN： 1873-1856
Classification of Quaternary Hermitian Self-Dual Codes of Length 20 Peer-reviewed

Masaaki Harada, Akihiro Munemasa

IEEE TRANSACTIONS ON INFORMATION THEORY　57　(6)　3758-3762　2011/06

DOI： 10.1109/TIT.2011.2134330 　

ISSN： 0018-9448
Classification of Generalized Hadamard Matrices H(6,3) and Quaternary Hermitian Self-Dual Codes of Length 18 Peer-reviewed

Masaaki Harada, Clement Lam, Akihiro Munemasa, Vladimir D. Tonchev

ELECTRONIC JOURNAL OF COMBINATORICS　17　(1)　2010/12

ISSN： 1077-8926
Pseudocyclic association schemes and strongly regular graphs Peer-reviewed

Takuya Ikuta, Akihiro Munemasa

EUROPEAN JOURNAL OF COMBINATORICS　31　(6)　1513-1519　2010/08

DOI： 10.1016/j.ejc.2009.08.003 　

ISSN： 0195-6698
On graphs with complete multipartite mu-graphs Peer-reviewed

Aleksandar Jurisic, Akihiro Munemasa, Yuki Tagami

DISCRETE MATHEMATICS　310　(12)　1812-1819　2010/06

DOI： 10.1016/j.disc.2009.12.009 　

ISSN： 0012-365X
CLASSIFICATION OF TERNARY EXTREMAL SELF-DUAL CODES OF LENGTH 28 Peer-reviewed

Masaaki Harada, Akihiro Munemasa, Boris Venkov

MATHEMATICS OF COMPUTATION　78　(267)　1787-1796　2009/07

DOI： 10.1090/S0025-5718-08-02194-7 　

ISSN： 0025-5718
A complete classification of ternary self-dual codes of length 24 Peer-reviewed

Masaaki Harada, Akihiro Munemasa

JOURNAL OF COMBINATORIAL THEORY SERIES A　116　(5)　1063-1072　2009/07

DOI： 10.1016/j.jcta.2008.11.011 　

ISSN： 0097-3165
There exists no self-dual [24,12,10] code over F(5) Peer-reviewed

Masaaki Harada, Akihiro Munemasa

DESIGNS CODES AND CRYPTOGRAPHY　52　(1)　125-127　2009/07

DOI： 10.1007/s10623-009-9271-5 　

ISSN： 0925-1022
Mass formula for even codes over Z_8、Cryptography and Coding Peer-reviewed

別宮耕一, 宗政昭弘

Springer LNCS 5921　65-77　2009
Mass formula for self-orthogonal codes over Zp2 Peer-reviewed

Rowena A. L. Betty, Akihiro Munemasa

Journal of Combinatorics, Information & System Sciences　34　51-66　2009
Mass Formula for Even Codes over ZZ(8) Peer-reviewed

Koichi Betsumiya, Rowena Alma L. Betty, Akihiro Munemasa

CRYPTOGRAPHY AND CODING, PROCEEDINGS　5921　65-+　2009

DOI： 10.1007/978-3-642-10868-6_5 　

ISSN： 0302-9743
On the Classification of Self-dual ZZ(k)-Codes Peer-reviewed

Masaaki Harada, Akihiro Munemasa

CRYPTOGRAPHY AND CODING, PROCEEDINGS　5921　78-+　2009

DOI： 10.1007/978-3-642-10868-6_6 　

ISSN： 0302-9743
A new example of non-amorphous association schemes Peer-reviewed

Ikuta Takuya, Akihiro Munemasa

Contributions to Discrete Mathematics　3　(2)　31-36　2008
Determination of weight enumerators of binary extremal self-dual [42,21,8] codes Peer-reviewed

Stefka Bouyuklieva, Masaaki Harada, Akihiro Munemasa

FINITE FIELDS AND THEIR APPLICATIONS　14　(1)　177-187　2008/01

DOI： 10.1016/j.ffa.2006.11.004 　

ISSN： 1071-5797
Simple abelian quadruple systems Peer-reviewed

Akihiro Munemasa, Masanori Sawa

JOURNAL OF COMBINATORIAL THEORY SERIES A　114　(6)　1160-1164　2007/08

DOI： 10.1016/j.jcta.2007.01.002 　

ISSN： 0097-3165
On the covering radii of extremal doubly even self-dual codes Peer-reviewed

Masaaki Harada, Akihiro Munemasa

ADVANCES IN MATHEMATICS OF COMMUNICATIONS　1　(2)　251-256　2007/05

ISSN： 1930-5346
Hyperplane partitions and Difference Systems of Sets Peer-reviewed

Ryoh Fuji-Hara, Akihiro Munemasa, Vladimir D. Tonchev

JOURNAL OF COMBINATORIAL THEORY SERIES A　113　(8)　1689-1698　2006/11

DOI： 10.1016/j.jcta.2006.03.014 　

ISSN： 0097-3165
Some restrictions on weight enumerators of singly even self-dual codes Peer-reviewed

M Harada, A Munemasa

IEEE TRANSACTIONS ON INFORMATION THEORY　52　(3)　1266-1269　2006/03

DOI： 10.1109/TIT.2005.864416 　

ISSN： 0018-9448
A characterization of designs related to an extremal doubly-even self-dual code of length 48 Peer-reviewed

Masaaki Harada, Akihiro Munemasa, Vladimir D. Tonchev

ANNALS OF COMBINATORICS　9　(2)　189-198　2005/07

DOI： 10.1007/s00026-005-0250-x 　

ISSN： 0218-0006
On some self-dual codes and unimodular lattices in dimension 48 Peer-reviewed

M Harada, M Kitazume, A Munemasa, B Venkov

EUROPEAN JOURNAL OF COMBINATORICS　26　(5)　543-557　2005/07

DOI： 10.1016/j.ejc.2004.06.013 　

ISSN： 0195-6698
A new quasi-symmetric 2-(56,16,6) design obtained from codes Peer-reviewed

A Munemasa, VD Tonchev

DISCRETE MATHEMATICS　284　(1-3)　231-234　2004/07

DOI： 10.1016/j.disc.2003.11.036 　

ISSN： 0012-365X
On a 5-design related to an extremal doubly even self-dual code of length 72 Peer-reviewed

M Harada, M Kitazume, A Munemasa

JOURNAL OF COMBINATORIAL THEORY SERIES A　107　(1)　143-146　2004/07

DOI： 10.1016/j.jcta.2004.03.005 　

ISSN： 0097-3165
Extremal self-dual [40,20,8] codes with covering radius 7 Peer-reviewed

M Harada, A Munemasa, K Tanabe

FINITE FIELDS AND THEIR APPLICATIONS　10　(2)　183-197　2004/04

DOI： 10.1016/j.ffa.2003.08.001 　

ISSN： 1071-5797
Spherical 5-designs obtained from finite unitary groups Peer-reviewed

A Munemasa

EUROPEAN JOURNAL OF COMBINATORICS　25　(2)　261-267　2004/02

DOI： 10.1016/S0195-6698(03)00111-2 　

ISSN： 0195-6698
Directed strongly regular graphs obtained from coherent algebras Peer-reviewed

M Klin, A Munemasa, M Muzychuk, PH Zieschang

LINEAR ALGEBRA AND ITS APPLICATIONS　377　83-109　2004/01

DOI： 10.1016/j.laa.2003.06.020 　

ISSN： 0024-3795
The nonexistence of certain tight spherical designs Peer-reviewed

Eiichi Bannai, Akihiro Munemasa, Boris Venkov

Algebra i Analiz　16　1-23　2004
Four-weight spin models and Jones pairs Peer-reviewed

A Chan, C Godsil, A Munemasa

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY　355　(6)　2305-2325　2003

DOI： 10.1090/S0002-9947-03-03253-7 　

ISSN： 0002-9947
On Hadamard matrices of order 2(p+1) with an automorphism of odd prime order p Peer-reviewed

DB Dalan, M Harada, A Munemasa

JOURNAL OF COMBINATORIAL DESIGNS　11　(5)　367-380　2003

DOI： 10.1002/jcd.10052 　

ISSN： 1063-8539
Type II codes over F-2+uF(2) and applications to Hermitian modular forms Peer-reviewed

E Bannai, M Harada, T Ibukiyama, A Munemasa, M Oura

ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG　73　13-42　2003

DOI： 10.1007/BF02941267 　

ISSN： 0025-5858
A mass formula for Type II codes over finite fields of characteristic two Peer-reviewed

A Munemasa

CODES AND DESIGNS　10　207-214　2002

ISSN： 0942-0363
A quasi-symmetric 2-(49,9,6) design Peer-reviewed

Masaaki Harada, Akihiro Munemasa

J. Combin. Designs　10　173-179　2002

DOI： 10.1002/jcd.10007 　
On Type II codes over F4 Peer-reviewed

Koichi Betsumiya, T. Aaron Gulliver, Masaaki Harada, Akihiro Munemasa

IEEE Trans. Inform. Theory　47　2242-2248　2001

DOI： 10.1109/18.945245 　
Type II codes over Peer-reviewed

Koichi Betsumiya, Masaaki Harada, Akihiro Munemasa

Lecture Notes in Comput. Sci.　2227　102-111　2001
Tight 2-designs and perfect 1-codes in Doob graphs Peer-reviewed

JH Koolen, A Munemasa

JOURNAL OF STATISTICAL PLANNING AND INFERENCE　86　(2)　505-513　2000/05

ISSN： 0378-3758
Classification of Type IV self-dual Z4-codes of length 16 Peer-reviewed

Masaaki Harada, Akihiro Munemasa

Finite Fields and Their Appl.　6　244-254　2000
Type IV self-dual codes over rings Peer-reviewed

Steven T. Dougherty, P. Gaborit, Masaaki Harada, Akihiro Munemasa, Patrick Sole

IEEE Trans. Inform. Theory　45　(7)　2345-2360　1999

DOI： 10.1109/18.796375 　
Duality maps of finite abelian groups and their applications to spin models Peer-reviewed

E Bannai, A Munemasa

JOURNAL OF ALGEBRAIC COMBINATORICS　8　(3)　223-233　1998/11

ISSN： 0925-9899
Orthogonal arrays, primitive trinomials, and shift-register sequences.

MUNEMASA A.

Finite Fields and Their Applications　4　252-260　1998

DOI： 10.1006/ffta.1998.0213 　
On fusion algebras associated to finite group actions Peer-reviewed

H Kosaki, A Munemasa, S Yamagami

PACIFIC JOURNAL OF MATHEMATICS　177　(2)　269-290　1997/02

ISSN： 0030-8730
The ter williger algebras of group association schemes Peer-reviewed

Eiichi Bannai, Akihiro Munemasa

Kyushu Journal of Mathematics　49　(1)　93-102　1995

DOI： 10.2206/kyushujm.49.93 　

ISSN： 1340-6116
ON PSEUDO-AUTOMORPHISMS AND FUSIONS OF AN ASSOCIATION SCHEME Peer-reviewed

T IKUTA, T ITO, A MUNEMASA

EUROPEAN JOURNAL OF COMBINATORICS　12　(4)　317-325　1991/07

ISSN： 0195-6698
ON NONSYMMETRIC P-POLYNOMIAL AND Q-POLYNOMIAL ASSOCIATION SCHEMES Peer-reviewed

A MUNEMASA

JOURNAL OF COMBINATORIAL THEORY SERIES B　51　(2)　314-328　1991/03

ISSN： 0095-8956
AN ANALOG OF T-DESIGNS IN THE ASSOCIATION SCHEMES OF ALTERNATING BILINEAR-FORMS Peer-reviewed

A MUNEMASA

GRAPHS AND COMBINATORICS　2　(3)　259-267　1986

ISSN： 0911-0119

Show all ︎Show first 5

Misc. 21

Antipodality of spherical designs with odd harmonic indices

Ryutaro Misawa, Akihiro Munemasa, Masanori Sawa

2024/10/12

More details Close

We determine the smallest size of a non-antipodal spherical design with harmonic indices $\{1,3,\dots,2m-1\}$ to be $2m+1$, where $m$ is a positive integer. This is achieved by proving an analogous result for interval designs.
Universal graph series, chromatic functions, and their index theory

Tsuyoshi Miezaki, Akihiro Munemasa, Yusaku Nishimura, Tadashi Sakuma, Shuhei Tsujie

2024/03/15

More details Close

In the present paper, we introduce the concept of universal graph series. We then present four invariants of graphs and discuss some of their properties. In particular, one of these invariants is a generalization of the chromatic symmetric function and a complete invariant for graphs.
Weakly distance-regular circulants, I

Akihiro Munemasa, Kaishun Wang, Yuefeng Yang, Wenying Zhu

2023/07/24

More details Close

We classify certain non-symmetric commutative association schemes. As an application, we determine all the weakly distance-regular circulants of one type of arcs by using Schur rings. We also give the classification of primitive weakly distance-regular circulants.
Constellations in prime elements of number fields

Wataru Kai, Masato Mimura, Akihiro Munemasa, Shin-ichiro Seki, Kiyoto Yoshino

2020/12/31

More details Close

Given any number field, we prove that there exist arbitrarily shaped constellations consisting of pairwise non-associate prime elements of the ring of integers. This result extends the celebrated Green-Tao theorem on arithmetic progressions of rational primes and Tao's theorem on constellations of Gaussian primes. Furthermore, we prove a constellation theorem on prime representations of binary quadratic forms with integer coefficients. More precisely, for a non-degenerate primitive binary quadratic form $F$ which is not negative definite, there exist arbitrarily shaped constellations consisting of pairs of integers $(x,y)$ for which $F(x,y)$ is a rational prime. The latter theorem is obtained by extending the framework from the ring of integers to the pair of an order and its invertible fractional ideal.
Primitive weakly distance-regular circulant digraphs

Akihiro Munemasa, Kaishun Wang, Yuefeng Yang

2019/08/23

More details Close

We classify certain non-symmetric commutative association schemes. As an application, we determine all the primitive weakly distance-regular circulant digraphs.
Self-Orthogonal Designs and Equitable Partitions (計算代数システムによる新しい数学の開拓と進展)

宗政昭弘

数理解析研究所講究録　(2012)　23-30　2016/12
Publisher: 京都大学数理解析研究所
ISSN： 1880-2818
Complex Hadamard matrices attached to some association schemes (Designs, Codes, Graphs and Related Areas)

Ikuta Takuya, Munemasa Akihiro

RIMS Kokyuroku　1956　137-152　2015/07
Publisher: Kyoto University
ISSN： 1880-2818
Steiner quadruple systems with abelian regular automorphism group (Finite Groups, Vertex Operator Algebras and Combinatorics)

Munemasa Akihiro

RIMS Kokyuroku　1656　55-64　2009/07
Publisher: Kyoto University
ISSN： 1880-2818
The Codes and the Lattices of Hadamard Matrices (Finite Groups and Algebraic Combinatorics)

Munemasa Akihiro, Tamura Hiroki

RIMS Kokyuroku　1593　154-161　2008/04
Publisher: Kyoto University
ISSN： 1880-2818
Self -Orthogonal Designs(Algebraic combinatorics and the related areas of research)

Munemasa Akihiro

RIMS Kokyuroku　1476　70-77　2006/03
Publisher: Kyoto University
ISSN： 1880-2818
Binary singly even self-dual code に関連した extremal problem(組合せデザインとその周辺における数理的基礎およびそれらの応用)

宗政昭弘

数理解析研究所講究録　1465　130-137　2006/01
Publisher: 京都大学
ISSN： 1880-2818
Spherical Designs

Akihiro Munemasa

Handbook of Combinatorial Designs, Second Edition　2006
Publisher: Chapman and Hall
Arithmetic and combinatories

A Munemasa

EUROPEAN JOURNAL OF COMBINATORICS　25　(4)　457-457　2004/05

DOI： 10.1016/j.ejc.2003.09.011 　

ISSN： 0195-6698
The 2000 Com (2)MaC conference on Association schemes, codes and designs - Preface

E Bannai, A Munemasa, SY Song, P Terwilliger

DISCRETE MATHEMATICS　264　(1-3)　1-1　2003/03

ISSN： 0012-365X
Spherical 5-Designs Obtained from the Unitary Group $U_{2m} (2)$ (Codes, lattices, vertex operator algebras and finite groups)

Munemasa Akihiro

RIMS Kokyuroku　1228　121-126　2001/09
Publisher: Kyoto University
ISSN： 1880-2818
Type II codes over $\mathbf{F}_2+u\mathbf{F}_2$ and an application to Hermitian modular forms (Algebraic Combinatorics)

Bannai Eiichi, Harada Masaaki, Munemasa Akihiro, Oura Manabu

RIMS Kokyuroku　1109　22-25　1999/08
Publisher: Kyoto University
ISSN： 1880-2818
New 5-designs with automorphism group PSL(2,23)

M Kitazume, A Munemasa

JOURNAL OF COMBINATORIAL DESIGNS　7　(2)　147-155　1999

ISSN： 1063-8539
Realizability of parameter sets for association schemes in terms of vertex independence problem

Munemasa Akihiro

RIMS Kokyuroku　962　81-85　1996/08
Publisher: Kyoto University
ISSN： 1880-2818
有限群の作用に付随したfusion algebra(代数的組合せ論)

宗政昭弘

数理解析研究所講究録　846　39-45　1993/06
Publisher: 京都大学
ISSN： 1880-2818
A local characterization of the graph of alternating forms

Munemasa Akihiro

RIMS Kokyuroku　840　121-123　1993/05
Publisher: Kyoto University
ISSN： 1880-2818
Fusion in Association Schemes

Munemasa Akihiro

RIMS Kokyuroku　768　23-28　1991/11
Publisher: Kyoto University
ISSN： 1880-2818

Show all ︎Show first 5

Presentations 43

Equiangular lines in dimension 18 and 1-factorization of K_{10} Invited

Akihiro Munemasa

Seminar Nasional Pendidikan Matematika dan Terapan　2025/07/11
A new two-distance set in the Euclidean space of dimension 23

Akihiro Munemasa

Waseda Workshop on Discrete Mathematics and Related Topics　2025/03/17
The regular two-graph on 276 vertices revisited Invited

Akihiro Munemasa

Genesis of Finite Simple Groups: 66 and 6　2024/12/01
Combinatorics of equiangular lines Invited

Akihiro Munemasa

Seminar at China University of Geosciences　2024/11/27
Combinatorics of equiangular lines Invited

Akihiro Munemasa

Colloquium at SUSTECH　2024/09/20
On Delorme's construction of distance biregular graphs Invited

Akihiro Munemasa

Discrete Mathematics Seminar at SUSTECH　2024/09/19
Flag-transitive 3-design from the action of PSL(2,q) on the projective line Invited

Akihiro Munemasa

G2C2, Hebei Normal University　2024/08/16
On the structure of $57$ equiangular lines \\ represented by norm $3$ vectors \\in the dual lattice of $A_9+A_9+A_1$ Invited

Akihiro Munemasa

INTERNATIONAL WORKSHOP ON SETS, DESIGNS, AND GRAPHS　2024/07/20
Locally amorphic distance-regular antipodal covers of complete graphs Invited

Akihiro Munemasa

The Ural Seminar on Group Theory and Combinatorics　2024/05/21
Abelian covers of association schemes with applications to SIC-POVM Invited

Akihiro Munemasa

Algebraic Graph Theory Seminar at University of Waterloo (online)　2024/04/22
Combinatorics of equiangular lines Invited

Akihiro Munemasa

2024/03/17
Locally amorphic distance-regular antipodal covers of complete graphs

Akihiro Munemasa

The 12th Workshop on Spectral Graph Theory　2024/01/27
Block-transitive 3-designs from PSL(2,q)

Akihiro Munemasa

Research on finite groups, algebraic combinatorics, and vertex algebras　2023/12/19
3-Designs from PSL(2,q) Invited

Akihiro Munemasa

2023/10/20
Jacobi polynomials and harmonic weight enumerators of the first-order Reed--Muller codes and the extended Hamming codes

Akihiro Munemasa

The 39th Algebraic Combinatorics Symposium　2023/06/19
Weakly distance-regular circulants Invited

Akihiro Munemasa

The 8th Workshop on Algebraic Graph Theory and its Applications　2023/03/03
On the shadows of the unimodular lattices constructed from ternary self-dual codes

Akihiro Munemasa

Orthogonal Designs and Related Combinatorics　2023/01/22
Sphere packings, root systems and signed graphs Invited

Akihiro Munemasa

Combinatorics Today Series, #9　2022/09/29
Introduction to Combinatorial Design Theory Invited

Akihiro Munemasa

ITB virtual course　2022/09/06
Association schemes, spin models and complex Hadamard matrices Invited

Akihiro Munemasa

CRM Workshop on Graph Theory, Algebraic Combinatorics and Mathematical Physics　2022/08/01
Quasi-Symmetric 2-(41, 9, 9) Designs and Doubly Even Self-Dual Codes of Length 40 Invited

Akihiro Munemasa

Hadamard 2020+2　2022/06/30
Quasi-symmetric 2-(41, 9, 9) designs

Akihiro Munemasa

The 38th Algebraic Combinatorics Symposium　2022/06/16
Extended double covers of non-symmetric association schemes of class 2 Invited

Akihiro Munemasa

The 6th Workshop on Algebraic Graph Theory and its Applications　2022/03/22
Semibiplanes and an inequality for incidence structures Invited

Akihiro Munemasa

Workshop on Algebraic Combinatorics　2022/01/25
Hermitian adjacency matrices of digraphs and root lattices over the Gaussian integers Invited

Akihiro Munemasa

Algebraic Graph Theory and Quantum Information　2021/08/23
Neighbor-balanced bijections of hypercubes Invited

Akihiro Munemasa

The 4-th Workshop on Algebraic Graph Theory　2021/03/01
Maximality of Seidel matrices and switching roots of graphs Invited

Akihiro Munemasa

2021 Ural Seminar on Group Theory and Combinatorics　2021/02/16
The regular two-graph on 276 vertices revisited Invited

Akihiro Munemasa

2020 Ural Workshop on Group Theory and Combinatorics　2020/08/24
The regular two-graph on 276 vertices revisited

Akihiro Munemasa

JCCA2020-DMIA2020-SGT9　2020/08/20
Extremal Finite Sets in Spheres and Projective Spaces Invited

Akihiro Munemasa

Indo Japan Joint Workshop on Quantum Computation and Information　2020/01/06
Group theoretic aspects of the theory of association schemes International-presentation

International Workshop on Algebraic Combinatorics　2016/10/28
Triply even codes obtained from some graphs and finite geometries International-presentation

Graphs and Groups, Spectra and Symmetries　2016/08/15
Self-orthogonal designs and equitable partitions International-presentation

Algebraic Combinatorics Workshop　2015/09/20
Extremal type II Z4-codes of length 24 and triply even binary codes of length 48 International-presentation

ICM2014 Satellite Conference on Algebraic Coding Theory　2014/08/12
Generalized tensor products and related constructions International-presentation

Workshop on Algebraic Design Theory and Hadamard Matrices　2014/07/10
Complex Hadamard matrices contained in a Bose-Mesner algebra International-presentation

Algebraic Combinatorics　2014/06/27
Godsil-McKay switching and twisted Grassmann graphs International-presentation

The Eighth Shanghai Conference on Combinatorics　2014/05/27
Twisted symplectic polar graphs International-presentation

Workshop on Algebraic Combinatorics　2013/11/20
Graphs with complete multipartite mu-graphs International-presentation

Incidence Geometry and Buildings　2012/02/06
Constructive enumeration of self-dual codes using tools from permutation groups International-presentation

International Conference on Coding and Cryptography　2011/08/25
Combinatorial structures derived from extremal even unimodular lattices International-presentation

Algebra and Combinatorics　2006/03
Extremal lattices and spherical designs International-presentation

Geometric and Algebraic Combinatorics 3　2005/08
Extremal lattices and spherical designs International-presentation

Com2MaC Conference on Association Schemes　2004/07

Show all Show first 5

Research Projects 50

spherical designs Competitive

System: The Other Research Programs

2003/04 - Present
algebraic coding theory Competitive

System: Basic Science Research Program

1998/01 - Present
algebraic graph theory Competitive

System: The Other Research Programs

1989/07 - Present
Evolution of Combinatorial Coding Theory

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Tohoku University

2023/04/01 - 2028/03/31
中心化代数のモノミアル表現，アダマール行列とアソシエーション・スキーム

宗政昭弘

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 特別研究員奨励費

Institution: 東北大学

2024/11/15 - 2026/03/31
Krein parameters in Q-polynomial association schemes and applications to design theory

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for JSPS Fellows

Institution: Tohoku University

2024/07/26 - 2026/03/31
整化可能な代数構造の代数的グラフ理論による特徴付け及び分類

谷口哲至, 宗政昭弘

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 基盤研究(C)

Institution: 広島工業大学

2021/04/01 - 2024/03/31

More details Close

令和3年度の研究計画では、整化可能整格子の一般化ホフマングラフによる特徴付けを行った。ある整格子の拡大で、従来のホフマングラフでは表せない整化可能整格子のクラスが幾つかある。そのクラスを列挙し一般化ホフマングラフで特徴付けを目指すことは、「グラフ」の言葉で代数構造の性質や構造の詳細を知ることができ、大変意義のある研究である。代数的グラフ理論や代数的組合せ論では、このような代数構造についての研究がなされており、その重要性を確かめることは容易である。また、Mohar氏らによる有向グラフのエルミート隣接行列の研究がある。令和3年度では、一般化ホフマングラフを用いて有向グラフ上のセゲディー型量子ウォークにおける遷移行列の型、及び周期的グラフを決定する研究をすすめた。ホフマングラフの大きな特徴はグラフの分解、及びそこから発生する既約性にある。それは逆に言うとある特徴をもったグラフの構成に役立つということである。既約性は最小構造を表し、これ自体でも興味深い対象である。このような周期性をもつグラフの構成手順をホフマングラフを利用することで得られるのであればとても意義のある重要な研究（１件実績あり）である。また、ホフマングラフついて周知を図る為に説明サイトの作成を目指すことも令和3年度に計画した。
Noncommutative association schemes, coherent algebras, their irreducible decompositions and applications

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Tohoku University

2020/04/01 - 2023/03/31
Eigenvalues of association schemes and characters of finite groups

Munemasa Akihiro

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Tohoku University

2017/04/01 - 2020/03/31

More details Close

Our main contribution is to demonstrate that fiber-commutative coherent configuration is a more natural generalization of commutative association schemes, than noncommutative association schemes. The reason why we believe fiber-commutative coherent configurations are more natural is that we can define canonically an analogue of eigenmatrix and Krein parameters. The well-known Krein condition can be generalized to positive semidefiniteness of matrices of Krein parameters for fiber-commutative coherent configurations. Fiber-commutative coherent configurations naturally appear as well-studied incidence structures, such as generalized quadrangles.
On Characterisations and Classifications of graphs by their Eigenvalues

Taniguchi Tetsuji

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Hiroshima Institute of Technology

2016/04/01 - 2020/03/31

More details Close

In this project, we have been studying on the structure of a generalized Bethe tree and a Hoffman graph. The structure of a generalized Bethe tree is hierarchical and symmetric, but it is very difficult to see the eigenvalues. With Segawa, Kubota, and Yoshie, we obtained results on the periodicity of the Grover Walk in the class. In addition, by generalizing the fat vertices and (signed) edges of a Hoffman graph, the Hoffman graph and generalized integral lattices can be associated. This makes it possible to explain the ingerability of generalized integral lattices. In problem of classifications of 3-lattices, we obtained the results that can be said to be the final goal on the line graph of the signed graph derived from integral lattices.
Comprehensive research on algebraic coding theory

Harada Masaaki, MIYAMOTO masahiko, KITAZUME masaaki, WADAYAMA tadashi, ARAYA makoto, BETSUMIYA koichi, OURA manabu, SHIMAKURA hiroki, TANAKA hajime, SUDA sho

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Tohoku University

2015/04/01 - 2019/03/31

More details Close

In this research project, I studied algebraic coding theory, especially, self-dual codes. I obtained results about the existence and the nonexistence of singly even self-dual codes. Moreover, I obtained results about linear complementary dual codes. These codes are a class of linear codes which are related to cryptography.
Various aspects of sporadic simple groups

KITAZUME MASAAKI, SAWABE Masato, MUNEMASA Akihiro, CHIGIRA Naoki, HARADA Masaaki, ABE Toshiyuki, SHIMAKURA Hiroki, NAKASORA Hiroyuki, HORIGUCHI Naoyuki, IRIE Yuuki, KOBAYASHI Yusuke

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Chiba University

2012/04/01 - 2018/03/31

More details Close

We have studied the Rudvalis simple group and related algebraic structures (code, lattice) and combinatorial structure (graph, design). Consequently we show the existence of even self-dual code preserved by the Rudvalis group, and give a combinatorial description of some generator. We further define five 2-designs by using a unitary group, and give a new construction of the Rudvalis graph from these 2-designs. We also consider Conway's theorem, which show the relation between the Rudvalis graph and the Hoffman-Singleton graph. Moreover we have completed the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups by showing non-existence of the remaining case.
Constructions of spherical designs using finite groups and lattices

Munemasa Akihiro

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Tohoku University

2014/04/01 - 2017/03/31

More details Close

In connection with spherical designs, we investigated spectra of graphs and finite permutation groups. We have found a highly nontrivial method of switching for constructing cospectral mates of graphs to give an alternative construction of the twisted Grassmann graphs. Other achievements includes extension of previously known properties of subsets of a sphere derived from association schemes.
グラフの最小固有値とユークリッド空間内の等角直線族

宗政昭弘, GREAVES GARY, GREAVES Gary

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 特別研究員奨励費

Institution: 東北大学

2014/04/25 - 2016/03/31

More details Close

代数的なアプローチにより、異なる固有値の数に制限をつけたグラフの分類問題に取り組んだ。特に、強正則グラフの一般化である、異なる固有値が３個しかないグラフの分類問題において、いくつかの成果が出た。正則グラフの場合はこの条件から自動的に強正則グラフになるが、正則でないが異なる固有値が３個しかないグラフは存在し、その分類問題にはわかっていないことが多い。この問題において、次数が２種類の二部グラフであるものについて分類結果を得た。また、等角直線族の存在問題の中から、正則グラフの存在問題に帰着できる場合を見いだし、実際に非存在を証明することができた。この問題に関しては、昨年度修正を終えた論文がようやく出版された。また、この論文で未だ未解決となっているひとつの場合について、グラフ理論の技術を使って解決する道筋を得た。特に、異なる固有値が４個しかない正則グラフの存在問題に帰着することができ、先行研究の成果を利用することができた。さらに、グラフのラプラス固有値のみたす不等式について、等号成立の条件を特徴付ける問題に取り組んだ。一般に等号成立の条件を完全に特徴付けることは困難であるが、いくつかの場合には完全な特徴付けが見つかり、また他のいくつかの場合には隣接行列を分割して得られる商行列の固有値の性質で特徴付けられることがわかった。これらグラフのラプラス固有値に関する研究成果をまとめた論文は執筆中である。
Challenging of the existence problem of a certain self-dual code through combinatorial designs and lattices

Harada Masaaki, MUNEMASA Akihiro, SHIMAKURA Hiroki

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Challenging Exploratory Research

Institution: Tohoku University

2014/04/01 - 2016/03/31

More details Close

In this project, I studied self-orthogonal designs including a self-orthogonal 5-(72,16,78) design, where the existences of such a design and an extremal doubly even self-dual code of length 72 are equivalent, with Akihiro Munemasa. Using the classification of unimodular lattices, I gave some classification of self-dual Zk-codes. In addition, I studied supplementary difference sets related to complex spherical 2-codes.
A elucidation of the structure of graphs by Algebraic Graph Theory and Spectral Graph Theory

Taniguchi Tetsuji, Seto Michio, Sano Yoshio, Tanaka Hajime

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

2013/04/01 - 2016/03/31

More details Close

By considering a graph as a matrix such as an Adjacency matrix or Laplacian matrix, we can study the structure with the linear algebra. In this research, we investigated the structure of graphs when eigenvalues are restricted, and challenged to explore a new research area by using the reproducing kernel Hilbert space theory. When considering the rough keyword "eigenvalue", there exist various mathematical research fields. When considering the discrete structure, it is because graph appear naturally. We have held research meetings every year to gather researchers who are studying graph eigenvalues in various mathematical areas and share information.
Constructions of complex Hadamard matrices using Algebraic Combinatorics and its applications

Ikuta Takuya, MUNEMASA AKIHIRO

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Kobe Gakuin University

2013/04/01 - 2016/03/31

More details Close

The aim of this research is to construct infinite series of complex Hadamard matrices, and more generally, type-II matrices, in the Bose--Mesner algebra of a certain symmetric association scheme. In particular, we recover the complex Hadamard matrices of order 15 found by Ada Chan. We compute the Haagerup sets to show inequivalence of resulting type-II matrices, and determine the Nomura algebras to show that the resulting matrices are not decomposable into generalized tensor products.
複素アダマール行列と関連した組合せ構造

宗政昭弘, SZOLLOSI Ferenc

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 特別研究員奨励費

Institution: 東北大学

2012/04/01 - 2015/03/31

More details Close

アダマール行列およびその一般化である複素アダマール行列は、数学のみならず様々な分野に応用を持つ。今年度は、weighing行列の構成と、モジュラーアダマール行列の構成について研究を行った。昨年完成し論文を投稿した実ユークリッド空間の等角直線族については、すでに好意的な査読結果を得ることができた。査読者の意見をもとに、修正版を作成し、投稿済みである。一方、グレブナー基底や最適化ソフトウェアを使い、これまで存在が未解決であったweighing行列の構成に成功した。これまで主に代数的な技術を使った構成法でカバーできない場合でも、ある程度の大きさのweighing行列が多変数関数の最適化問題に帰着して数値計算により求まることがわかったことは今後の研究方針にも影響を与えることになった。これらの研究成果はカナダにおける国際会議で発表した。さらに、R. Craigen 氏との３人の共著によりBelevitchによるweighing行列の構成法を複素アダマール行列へ応用する方法について共著論文を準備中である。この構成法はTurynにより一般化されたものの、記述が困難であったが、包除原理を用いた新たな方法によって明解な記述法が最近得られた。これにより、Turynの定理を一般化することに成功した。生田卓也氏との３人の共著によりクラス３のアソシエーション・スキームから得られる複素アダマール行列の構成法について共著論文を準備中である。特に、アモルフィックな場合には無限個の複素アダマール行列がひとつのアソシエーション・スキームから得られることがわかっている。
A New Development of Algebraic Coding Theory

HARADA Masaaki, MUNEMASA Akihiro, KITAZUME Masaaki, WADAYAMA Tadashi, ARAYA Makoto, HAGIWARA Manabu

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

2011/04/01 - 2015/03/31

More details Close

In this research project, I studied algebraic coding theory, especially, self-dual codes. As results, classifications of self-dual codes of length 36 and doubly even self-dual codes of length 40 are completed. Also, I considered the construction of extremal self-dual Z2k-codes.
Analytic, Algebraic and Combinatorial studies on continued fractions

KOMATSU Takao, MUNEMASA Akihiro, AKIYAMA Shigeki, TANAKA Takaaki

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Hirosaki University

2010/04/01 - 2014/03/31

More details Close

Analytic studies of continued fractions are to obtain exact algebraic expressions for approximation evalucations of various Hurwitz and Tasoev continued fractions, some relations between Fibonacci-zeta functions and continued fractions, and some relations between zeta functions and Cauchy polynomials. Algebraic studies of continued fractions are to obtain independence measures of arithmetic functions and to construct Liouville numbers in non- Archimedean case. Combinatorial studies of continued fractions are to give upper bounds on cyclotomic numbers, and to discover linear recurrence relations associated with multinomial Pascal triangles. In addition, cross-studies of continued fractions are to show some relations among continued fractions, Fibonacci numbers and congruent numbers, and to discover the concept of poly Cauchy numbers and polynomials as some generalizations of Cauchy numbers, which are related with Bernoulli numbers.
最小固有値に制限を加えたグラフの研究

宗政昭弘, GREAVES Gary

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 特別研究員奨励費

Institution: 東北大学

2012 - 2013

More details Close

最小固有値が-3以上であるグラフ全体がどのような構造を持つか理解することを目標としていた。まず最小固有値が-3より真に大きいホフマングラフを解析するために、最小固有値が-2より真に大きいグラフの辺に符号をつけたグラフを考察した。このようなグラフの中には木のライングラフがあり、その最小固有値の振る舞いに関するホフマン予想を昨年度肯定的に解決していた。今年度は、それをさらに一般化して定式化し、その証明も与えた。辺に符号をつけたグラフは最小固有値が-3以上であるホフマングラフから自然に得られ、この成果は最小固有値が-3より真に大きいグラフの分類へ大きな一歩となると考えられる。この研究成果は6月に静岡大学で、7月に英国で学会発表を行い、9月に論文を完成させて学術雑誌に投稿済みである。また10月以降は等角直線族の研究を始め、特に直線族の表すサイデル行列の固有値に注目した研究を行なった。固有値が代数的整数であること、行列式の偶奇に注目することで固有値の可能性に制限を与えることを利用して、過去に知られていた14次元における等角直線族の最大数の上界を改良することに成功した。この研究成果は11月に中国と日本で、1月に韓国でそれぞれ発表を行なった。2月になってさらなる研究の進展があり、他の次元においても上界の改良が可能であることがわかった。この結果をすべて含めた論文が3月に完成し、学術雑誌に投稿済みである。
Algebraic coding theory and combinatorial designs

HARADA Masaaki, MUNEMASA Akihiro, KITAZUME Masaaki, ARAYA Makoto

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Yamagata University

2008 - 2010

More details Close

The main aim of this research is to study self-dual codes, which are of interest from an algebraic point of view. In self-dual codes, it is a fundamental problem to classify these codes. We completed classifications of several types of self-dual codes using some different approaches. We constructed extremal self-dual codes which have the largest minimum weights among all self-dual codes of that length. Using self-dual codes, we also studied combinatorial designs.
Research on algebraic coding theory and its applications for vertex operator algebras

BETSUMIYA Koichi, MUNEMASA Akihiro, HARADA Masaaki, YAMAUCHI Hiroshi, SHIMAKURA Hiroki, LAM Ching Hung

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Jobu University

2007 - 2010

More details Close

We have presented an efficient algorithm for finding triply even codes by investigating the structure of triply even codes. This algorithm has produced a classification of maximal triply even codes of length up to 48. As a result, we have found a new maximal triply even code which is contrary to the expected behavior constructed by a triangular graph. Moreover, new framed vertex operator algebras have been constructed from the list of codes.
Study on algebraic or combinatorial structures whose automorphism groups contain finite simple groups

KITAZUME Masaaki, NOZAWA Sohei, KOSHITANI Shigeo, SAWABE Masato, SUGIYAMA KenーIchi, ANDO Tetsuya, YAMADA Hiromichi, MUNEMASA Akihiro, HARADA Masaaki, CHIGIRA Naoki, ABE Thoshiyuki

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Chiba University

2007 - 2010

More details Close

We have studied some algebraic structures and combinatorial structured whose automorphism groups contain finite simple groups. (1) We have studied the binary code spanned by the sets of fixed points of the involutions of a finite transitive permutation group and its dual code. New self-dual codes invariant under the Hall-Janko group and the Rudvalis group have been constructed, respectively. (2) We have studied rank 3 graphs related to some sporadic simple groups (especially, HJ, Suz, M24). New constructions of these rank 3 graphs from some designs have been obtained. (3) We have determined the minimum value m such that a given Niemeier lattice is a m-neighbor of the Leech lattice.
Representations of Terwilliger algebras and their applications

ITO Tatsuro, BANNAI Eiichi, MUNEMASA Akihiro, HIRAKI Akira, SUZUKI Hiroshi, YOSHIARA Satoshi, NOMURA Kazumasa, TANABE Kenichiro, KAWAGOE Kenichi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Kanazawa University

2006 - 2009
Applications of algebraic methods in coding theory to combinatorial designs and discrete geometry

MUNEMASA Akihiro, HARADA Masaaki, TANIGUCHI Tetsuji, IMAI Hideo, URAKAWA Hajime, ASOH Toru, TAYA Hisao, BETSUMIYA Koichi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Tohoku University

2005 - 2008
Synthetic study of algebraic combinatorics

BANNAI Eiichi, BANNAI Etsuko, KOIKE Masao, MUNEMASA Akihiro, ITO Tatsuro, SUZUKI Hiroshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Kyushu University

2004 - 2007

More details Close

One of the goal of this grant was to widely contribute to the advancement of algebraic combinatorics in Japan through the financial support for conferences and workshops. During the fiscal year 2004-2007, the grant was used to partly support The 21st, 22nd, 23rd, 24th Algebraic Combinatoric Symposiums(Shinshu University, Ehime University, Tobhiku University, Ehime University), annual symposiums at RIMS, two COE Workshops on Sphere Packings, held at Kyushu University, and Mini-symposiums on algebraic combinatorics(three at Kyushu university and one in Kobegakuin University), etc. We also held 4 Japan-Korea workshops on Algebra and Combinatorics, and contributed to the international relations and cooperations. Research in Algebraic Combinatorics in Japan is showing steady progress. The progress covers diverse areas such as distant-regular graphs, association schemes, codes, designs, lattices, modular forms. The recent research of the principal investigator is focused on the study of Euclidean designs. Collaborating with Etsuko Bannai, we obtained the classification of tight 4-designs with constant weight, the classification of Gaussian tight 4-designs, and the classification of optimal tight 4-designs on two concentric spheres. In addition, jointly with Suprijanto, we succeeded in showing that we can get new tight Euclidean designs starting from some tight Euclidean designs. Our recent work includes the classification of tight Euclidean 7-designs on two concentric spheres. We have also proved that any antipodal t-design of degree s with t$2s-3 has the structure of Q-polynomial association scheme, and found such new examples with t=5 and s=4 from maximal real MUB. We started to study how coherent configurations are attached to tight Euclidean designs. We succeeded in proving the uniqueness of two association schemes related to universally optimal codes in the sense of H. Cohn (Bannai-Bannai-Bannai), and have shown, jointly with Abdukhalikov and Suda, that higher dimensional analogues of one of them are obtained from maximal real MUB.
Research on ideal class groups of algebraic number fields and number theoretic functions and its applications

TAYA Hisao, MUNEMASA Akihiro, IMAI Hideo

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Tohoku University

2004 - 2006

More details Close

The purpose of this research is to develop the fundamental theory of ideal class groups of algebraic number fields further, especially taking account of Iwasawa theory. Though we did not find out a theoretical behavior of p-ambiguous ideal class groups in the first year of this research, we verified that our estimate on the density of real quadratic fields whose Iwasawa invariants for p=3 are all zero is very near to the conjectural ratio obtained by modifying Cohen-Lenstra Heuristics on class numbers. As compared with the case p>3 in which known estimates are too far from the conjectural one, our analysis is interesting. Next year, we showed that the density of real quadratic fields whose Iwasawa invariants for p=2 are all zero is zero. This is also interesting, because the density for p=3 is more than 0.7 by our previous result and the one for p>3 is conjectured to be positive. From that time to the last year of this research, we had an opportunity to have a joint research with Dr. Gen Yamamoto (Tokyo Denki University) and determined all real abelian 2-extension fields whose Iwasawa invariants for p=2 are all zero, by using genus theory and the theory of central extensions. The results obtained in this research are presented in some of conferences like as Korea-Japan Number Theory Seminar and ICM2006. Though we did not get a satisfying result about mutual application between number theory and combinatorial theory unfortunately, we played an important role in posing and solving common problems in both fields by organizing mini conferences where researchers in both fields gathered
Global analysis of the heat kernels on Riemannian manifolds and graphs

URAKAWA Hajime, ASOH Tohl, MUNEMASA Akihiro, KANEKO Makoto, OBATA Nobuaki, ITOH Jin-ichi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Tohoku University

2004 - 2006

More details Close

The heat kernels of compact Riemannian manifolds converge to the equilibrium when time goes to infinity. We studied the rates of the heat kernels how do they reflect from the geometric structures of Riemannian manifolds. We showed the convergence rates are Lipshitz continuous on the deformation of Riemannian manifolds, we gave their upper estimation in terms of Ricci curvature and diameter, and also the upper estimation in terms of the non-zero first eigenvalue of the Laplacian. We gave their precise lower and upper estimations in the case of compact Riemannian symmetric spaces of rank one. A Yang-Mills connection is a critical point of the Yang-Mills functional, and this is an analogue of harmonic map which is a critical point of the energy functional. Recently, the notion of biharmonic map was introduced which is a critical point of the 2-energy functional. We introduced the notion of 2-Yang-Mills connection which is a critical point of the 2-Yang-Mills functional. This notion is a natural generalization of Yang-Mills connection, and many further studies would be expected. We introduced quite new method to visualize the Dirichlet or Neumann boundary eigenvalue problem of the Laplacian on plane domains. This method improved 20 percents fast comparing the known methods and reduced many steps input the data into computers. This new method made visualizations of the eigenvalue problems of the Laplacian on compact surfaces and bounded three dimensional domains. We applied to get patent of this method for programming of computer.
Finite Simple Groups and Related Codes, Lattices and Vertex Operator Algebras

KITAZUME Masaaki, KOSHITANI Shigeo, NOZAWA Sohei, SUGIYAMA Ken-ichi, HARADA Masaaki, CHIGIRA Naoki

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Chiba University

2003 - 2006

More details Close

We have studied codes, lattices and vertex operator algebras related to finite simple groups. Main results are as follows : 1. We studied singly even codes of length 48 and odd unimodular lattices of rank 48 which have (resp. do not have) extremal neighbors. As a byproduct, we have constructed a new extremal code over Z/4Z. 2. We studied a putative extremal binary code of length 72. We showed that if there is a self-orthogonal 5-(72,16,78) design then the rows of its block-point incidence matrix generate an extremal doubly-even self-dual code of length 72. 3. We constructed new self-dual codes of length 100 invariant under the Hall-Janko group. We studied the binary code C(G, n) defined as the dual code of the code spanned by the sets of fixed points of involutions of a given group G. We showed that any G-invariant self-orthogonal code of length n is contained in C(G, n). Many self-orthogonal codes related to sporadic simple groups, including the extended Golay code and the above code for the Hall-Janko group, are obtained as C(G, n). Some new self-dual codes invariant under sporadic almost simple groups are constructed. 4. We constructed extremal singly even self-dual [64,32,12] codes with weight enumerators which were not known to be attainable. In particular, we find some codes whose shadows have minimum weight 12. By considering their doubly even neighbors, extremal doubly even self-dual [64,32,12] codes with covering radius 12 are constructed for the first time. 5. We studied maximum cocliques of sporadic rank 3 graphs and related designs. We gave some reconstructions of the Hall-Janko graph from the Witt system and the hexacode. Moreover we considered the maximum coclique design of the sporadic Suzuki graph. We constructed a new 3-(66,16,21) design with the automorphism group U_{3}(4):4, the unitary group over the 16-element field. By using this design, we gave a new construction of the sporadic Suzuki graph.
誤り訂正量子符号の有限群論的アプローチ

北詰正顕, 杉山健一, 桜井貴文, 野澤宗平, 宗政昭弘, 原田昌晃, 大坪紀之

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 萌芽研究

Institution: 千葉大学

2002 - 2004

More details Close

(1)本年度においては,まず,Calderbank-Rains-Shor-Sloaneの仕事との関連から重要であると思われるGF(4)上の(特に線形でない)符号の構成について考えた。分担者の宗政・原田とは,前年度までの方針に則り48次元のunimodular latticeから得られる長さ24の非線形符号の構成を試みたが,条件の良いlatticeを見つけることができず成果を得るには至らなかった。この研究の過程から副産物として得られた48次元の符号と格子に関する結果は論文として公表した。そこでは,特に,剰余整数環Z/4Z上の新しい(良い)符号を発見している。このような剰余整数環上の符号と,4元体上の符号,あるいは,量子符号,との関連も模索したが,はっきりしなかった。 (2)分担者の杉山とは,代数幾何符号の観点からのアプローチを検討した。その結果,柴木氏(岩手県立宮古短期大学)の協力を得て,特異点を持つ代数曲線から、線形符号を作る方法を得た。この方法は構成が簡単で、さらに復号化もしやすいという利点をもつ。これについては,論文として準備中である。この方法は色々な体に適用できるため,GF(4)の場合について検討を加えたが,現時点では良い符号を得ることは出来なかった。 (3)最後に,本研究の「有限群論的アプローチ」という精神を生かすべく,符号に(大きな)有限群が作用するという条件を積極的に使うような理論を考えてみた。その結果,千吉良直紀氏(室蘭工業大学)の研究協力を得て,GF(2)上の(すなわち古典的)符号についてはある種の上限を与える定理を得て,学会発表を行い,論文として準備している。これを他の体(特にGF(4))について拡張することは,今後の課題であると考える。
A study of the interacting area among the theory of quadratic forms and the theory of modular forms and the algebraic coding theory

OZEKI Michio, KITAZUME Masaaki, MUNEMASA Akihiro, HARADA Masaaki, SAWADA Hideki, MURABAYASHI Naoki

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Yamagata University

2002 - 2004

More details Close

The present research has been done in the period between year 2002 and 2004 under the GRANT-IN-AID sponcered by the Ministry of Education, Culture, Sports, Science and Technology. In the application the head investigator raised five reseach purposes : (1)a study of the ineraction between the coding theory and the theory of modular forms, (2)a study of the lattices constructed from the binary self-dual code and the tertiary self dual codes, (3)the covering radius problem for the n-dimensional lattices, (4)the covering radius problem for non self-dual linear codes, (5)an interaction bewtween the coding theory and the cryptology. As to the purpose (1) we get some results and gave 4 talks and are preparing the research papers. As to (2) we have published one research paper and are preparing one paper. As to (3) the result is not mature for writing a paper. As to (4) we gave two talks and are preparing some research papers. There is no actual activity fot the purpose (5). Besides the research purpose we have published three research papers.
Comprehensive study on Algebraic Combinatorics

BANNAI Eiichi, MUNEMASA Akihiro, BANNAI Etsuko, ITO Tatsuro, SUZUKI Hiroshi, KOIKE Masao

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Kyushu University

2001 - 2003

More details Close

One of the goal of this grant is to widely contribute to the advancement of algebraic combinatorics in Japan through workshops and travel aid. During the fiscal year 2001-2003, the grant was used to partly support : The 18th, 19th, 20th Algebraic Combinatoric Symposiums (at resp. Chiba University, Kumamoto University, Hokkaio University), three symposiums entitled "Algebraic Combinatorics" at RIMS, three workshops on areas related to automorphic forms at Hamamatsu (Ibukiyama, Bannai, Saito, Miyamoyo organizers). Symposium at Yamagata (Nov. 2002), International Conference EA- CAC2 held in Fukuoka (Bannai organizer, Nov. 2003). Research in Algebraic Combinatorics in Japan is showing steady progress. The progress covers diverse areas such as distant-regular graphs, association schemes, codes, designs, lattices, modular forms. The results of the principal invstigator includes: (i) Character tables of commutative association schemes and Ramanujan graphs, (ii) Relations between codes, lattices and modular forms, (iii) Tight 4-, 5-, 7-designs on spheres (Bannai Munemasa-Venkov), (iv) Tight designs/codes over Grassmanian spaces (Bachoo-Bannal Coulangeon). In addition, the pricinpal investigator studied designs on Euclidean spaces: Collaborating with Etsuko Bannai, the classification of tight 4-designs with constant weight, the classification of Gaussian tight 4-designs, and the classification of optimal tight 4-designs on two concentric spheres were completed. We are currently challenging more general classi-fications. Jointly with Makoto Tanabe, we participated in the verification of Oleg Musin's spectacular result: The determination of the Kissing number in dimension four, and helped the completion of Musin's proof.
ALGEBRAIC CODING THEORY, COMBINATORIAL DESIGNS AND ASSOCIATION SCHEMES

MUNEMASA Akihiro, URAKAWA Hajime, BANNAI Etsuko, BANNAI Eiichi, HIRAKI Akira, HARADA Masaaki

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

2000 - 2003

More details Close

A generalization of the concept of a type II code has been obtained for arbitrary finite fields of characteristic two, and the mass formulas for such codes have been obtained. This allowed us to classify nearly all type II codes whose binary lengths are at most 32, and our results were presented in the 14th AAECC symposium in Australia. We have solved a long standing problem of the existence of tight spherical designs, and this result was presented in an international conference on combinatorics in the Netherlands in 2002.Our result uses the theory of modular forms, and we participated in an international conference on modular forms in 2004 in order to find more connections between combinatorics and the theory of modular forms. We also explored the connections between integral lattices with binary codes, and spherical designs with ordinary combinatorial designs. We have established a uniqueness of a certain self-orthogonal 5-design related to a binary self-dual code, and we have submitted a paper about this result.
Finite Simple Groups and Related Codes, Lattices and Vertex Operator Algebras

KITAZUME Masaaki, SUGIYAMA Ken-ichi, NOZAWA Sohei, KOSHITANI Shigeo, HARADA Masaaki, YAMADA Niromichi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Chiba University

2000 - 2002

More details Close

We have studied codes, lattices and vertex operator algebras related to finite simple groups. Main results are as follows : 1.The classifications of the 2-and 3-radical subgroups of Fischer's simple groups F_<22>, F_<23>, F'_<24> have been completed. 2.Even unimodular Gaussian lattices of dimension 12 have been classified. 3.A sufficient condition for extremal Z_6-codes, and as an application, many Z_6-code related the Leech lattice had been constructed. Moreover the self-dual Z_6-codes of length 8 are classified. 4.The construction method of unimodular lattices using ternary self-dual codes has been studied. Extremal odd unimodular lattices in dimensions 44, 60 and 68 are constructed for the first time. 5.The constructions of vertex operator algebras using Z_8-codes and subalgebras V_<√<2>A_3> have been considered. We also give a complete decomposition of the Moonshine VOA V^* associated with some subalgebra given by an embedding of the lattice (√<2>A_3)^8 into the Leech lattice. 6.By using Z_3-orbifold construction given by Dong-Mason, we give a complete decomposition of the Moonshine VOA V^* associated with some subalgebra given by an embedding of the lattice (√<2>A_2)^<12> the Leech lattice. We also give the explicit actions of certain 3A-elements of the Monster simple group on V^* are defined.
Association schemes and spin models

BANNNAI Etsuko, ITO Tatsuro, MUNEMASA Akihiro, BANNAI Etsuko, NOMURA Kazumasa

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: KYUSHU UNIVERSITY

1998 - 2001

More details Close

The main purpose of this research was to find out sets of points with finite cardinality with a "good" configuration through investigation of relations between spin models and association schemes. Association scheme is the one of the most important objects in the study of algebraic combinatorics. On the other hand spin models give topological invariants of the knots and links in the 3 dimensional Euclidean space R3. During the period we received this grant we obtained the following results. (1) We found that Bose-Mesner algebras attached to a 4-weight spin model coincide with a unique Bose-Mesner algebras. (2) We tried to classify 4-weight spin models with small size and obtained some partial results. (3) We found out that the existence of a 4-weight spin model with exactly two valued on W_2 is equivalent to the existence of a symmetric design with some polarity. (4) We defined type II codes on finite abelian groups using the solutions of modular invariance equations of finite abelian group association schemes. The solutions of this modular invariance equations are known to give spin models. (5) We found out that a upper bound for the cardinality of an s-distance set in Euclidean spaces coincides with the lower bound for the cardinality of 2s-design given by Delsarte-Seidel. In particular we found out that if we assume that s-distance set is antipodal, then a upper bound coincides with the lower bound for the cardinality of antipodal 2s - 1-design given by Delsarte-Seidel. However the situation is different from the spherical case. The grant we received was mainly used for the travel expenses of us and also the re-searchers in Japan or oversea who are working on related subject with our research. We could make important discussions with many researchers in related topics. We could organized "Mini Conference on Algebraic Combinatorics" at Kyushu University 4 times.
Representations of TerwiUiger algebras and their applications

ITO Tatsuro, NOMURA Kazumasa, MUNEMASA Akihiro, YAMADA Mieko, HIRAKI Akira, YASHIARA Satoshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Kanazawa University

1998 - 2001

More details Close

The major outcome of this research project, which will be discussed in detail later, is that there was a breakthrough in the area of the non thin representations of Terwilliger algebras of P- and Q- polynomial type. Among others are some pioneering works on the Terwilliger algebras of cyclotomic schemes and the Jacobi sums, on relations between spin models, quantum groups and Terwilliger algebras, on the structure of type II matrices. Let T be a Terwilliger algebra of P- and Q-polynomial type with classical parameters, where the classical parameters mean the ones with one less variables than usual. We obtained the following results. The irreducible T-modules of endpoint 1 have a ladder basis (Hobart-Ito). In the simplest case of parameters, irreducible T-modules are determined via finite dimensional irreducible representations of On sager algebras (Ito-Tanabe-Terwilliger). A basic theorem is obtained for the structure of T-modules, enabling us to deal with the general case by defining the q-analogue of an On sager algebra (q-On sager algebra) (Ito-Tanabe-Terwilliger). Thus in the case of classical parameters, the problem of irreducible T-modules is reduced to the determination of finite dimensional irreducible representations of q-Onsager algebras. If the diameter is 3, finite dimensional irreducible representations of q-0n sager algebras are determined via the type (1,1) representations of the affine quantum algebra U_q (sl_2). This is the breakthrough mentioned at the beginning and we are aiming at generalizing it to arbitrary diameters.
A collective study of algebraic combinatorics

BANNAI Eiichi, MUUEMOSA Akihiro, KOIKE Masao, BANNAI Etsuko, YAMAHI Hiroyoski, SUZUKI Hiroshu

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (A).

Institution: KYUSHU UNIVERSITY

1997 - 2000

More details Close

The main purpose of this grant was to support the overall developments of the research in algebraic combinatorics in Japan, by supporting the expenses of speakers and participants who attended the symposiums in this and related areas. Each year, we have about 2 large meetings and some smaller workshops. These large meetings were : the 14th (Mitaka, Tokyo), 15th (Kanazawa), 16th (Fukuoka) and 17 th (Tsukuba) Algebraic Combinatorics Symposiums ; and the conferences on algebraic combinatorics and/or related subjets which were held in RIMS annually for the last several years. The current activities of algebraic combinatorics in Japan is very active and successful. We have had quite notable developments, in particular, on the subjects such as classification problems of association schemes and distance-regular graphs ; on spherical designs, on spin models, and on Terwilliger algebras and its connections with representation theory. One of the main research subjects in the close neighborhood of the principal investigator has been the study of codes over various finite rings and finite abelian groups, and then to apply these results to the studies of modular forms. We have obtained various results on self-dual codes and Type II codes over various rings. In addition, we have classified the finite index subgroups of SL (2, Z) whose ring of modular forms is isomorhpic to a polynomial ring. We have also started the study of modular forms of fractional weights, and then we found an interesting result (Bannai-Koike-Munemasa-Sekiguchi) on the modular forms of weghts 1/5-integers of Γ (5). We are currently continuing to work on further generalizations in this direction. The principal investigator has also started to work on the character tables of association schemes and trying to look at the object, by looking at them as a finite version of modular forms. Also, the principal investigator has started to study the modular data of finite groups as well as their modular invariants.
Pseudorandom numbers and their Application to Stochastic Numerical Analysis

TAKASHIMA Keizo, OGAWA Shigeyoshi, HOTTA Ryoushi, TAKENAKA Shigeo, MUNEMASA Akihoro, HIKIDA Masato

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

Institution: Okayama University of Science

1998 - 1999

More details Close

We introduce statistical tests for pseudorandom number generations, which are based on functionals of sample paths of 1-dimensional random walks. Using these methods, we test statistically the following pseudorandom number generators : m-sequences, additive number generators, and cellular automata generators. The results of random walk tests detect statistical biases of these generators. Moreover, from the results, we can find some conjectures, for example, ● the multiples of a trinomial f over GF(2) are only those having the form such as square of f and so on, while the degrees of multiles are not so large. This conjecture has been proved by Munemasa, in case that the degree of multiples are less than or equal to the twice of the degree of f. ● A primitive polynomial over GF(2) and its reciprocal polynomial must have different algebraic properties. This conjecture is assured by the results of maximum tests, and sojourn time tests.
Finite Groups (Sporadic Simple Groups) and Related Topics

KITAZUME Masaaki, SUGIYAMA Ken-ichi, NOZAWA Sohei, KOSHITANI Shigeo, MUNEMASA Akihiro, MIYAMOTO Masahiko

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Chiba University

1997 - 1999

More details Close

We have studied finite simple groups and related graphs, designs, codes, lattices and vertex operator algebras. Main results are as follows : 1. The 2- and 3-radical subgroups of Fischer's simple groups FィイD222ィエD2, FィイD223ィエD2, F'ィイD224ィエD2 have been classified. 2. Two kinds of non-split extensions of OィイD27ィエD2(3) have been constructed explicitly by using Dickson's trilinear form and some special Moufang loop. 3. By using a lattice VOA, a new proof of the Borwein identity has been given. 4. New VOAs related to ternary codes have been introduced, and the irreducible representations of L(ィイD74(/)5ィエD7, 0) 【symmetry】 L(ィイD74(/)5ィエD7, 3) have been determined. 5. By using an embedding ィイD82ィエD8AィイD312(/)2ィエD3 into the Leech lattice and a ZィイD22ィエD2 × ZィイD22ィエD2-code, some decomposition of the Moonshine VOA has been given. 6. Some 5-designs invariant by PSL(2, 23) and related to S(5, 8, 24) have been classified. 7. A simple characterization of S(5, 8, 24) (or Golay code) has been given. 8. The Niemeier lattices have been constructed form ZィイD24ィエD2-codes, and their embeddings of them into 1/ィイD82ィエD8 times the Leech lattice have been given. 9. The exceptional graphs embedded into the root system EィイD28ィエD2 have been classified. 10. Even unimodular Gaussian (resp. Quaternionic) lattices of dimension 12 (resp. 6) have been classified.
有限体上の交代形式の幾何学的研究

宗政昭弘, 関根嘉浩, 坂内悦子, 山田美枝子

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 基盤研究(C)

Institution: 九州大学

1996 - 1996

More details Close

有限群の作用する等質空間の一般化としてアソシエーション・スキームとそれに付随する代数のその表現論、関連した組合せ的構造を研究している。特に、アソシエーション・スキームの持つ代数的特徴を一般化したものであるC-algebraに似た概念としてfusion algebraというものがあるが、必ずしもアソシエーション・スキームからではなく、しかも有限群から、まったく別の方法で面白いfusion algebraが構成できることがわかり、このことは有限群の群環のguantum doubleに対応するものであることがわかった。さらにそれを有限群の一般の等質空間に対しても定義したいと考えた末、群上のベクトルバンドルという言葉を使って記述することができた。このことは、研究分担者である関根氏の助言により、すでに関連した研究を作用素環論の分野において行っている幸崎、山上両氏との共著の論文になった。また、研究分担者である山田、坂内両氏はアソシエーション・スキームとスピンモデルについての研究を活発に続けており、成果をいくつもの研究集会で発表した。さらにアーベル群上のスピンモデルについては、分類の最終的決着とも言える論文を、宗政・坂内の共著で準備中である。有限体上の交代形式のつくるアソシエーション・スキームについては、その自己同型群が自明でない正則正規部分群をもつことがわかっており、ここでは一歩進んでそのような部分群を完全に分類することを目標に研究が進行中である。この分野における専門家であるM.Muzychuk氏を2週間招へいしたことは、研究の進展にはずみがついただけでなく今後の研究方針を考える上でも大変有意義であった。
Research on association schemes and related topics

BANNAI Eiichi, SHIRATANI Katsumi, KATO Mitsuyoshi, BANNAI Etsuko, MUNEMASA Akihiro

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: KYUSHU UNIVERSITY

1995 - 1996

More details Close

The head researcher has done the research in the following 3 directions. 1.Study of spin models. (i) We introduced the concept of 4-weight spin models, and proved that link invariants are obtained from them (joint work with Etsuko Bannai). (ii) We gave the complete classifications of the dualities and the modular invariances on the character tables of finite abelian groups, and proved that spin models are constructed from such solutions (joint work with Etsuko Bannai and F.Jaeger). 2.Construction of various automorphic forms from either the weight enumerators of codes or polynomial invariants of certain finite groups. (i) We proved that Jacobi forms are constructed from the simultaneous diagonal actions of the 2-dimensional unitary reflection group of order 192 (No.9 in Shepherd-Todd's list)(joint work with Michio Ozeki).(ii) Explicit constructions of certain Jacobi forms of weight 4 (joint work with Michio Ozeki and Shinri Minashima). (iii) We determined the explicit basis of the polynomial invariants mentioned in (i) above (joint work with Etsuko Bannal, Michio Ozeki and Yasuo Teranishi).(iv) We are currently studying Type II additive codes on finite abelian groups (joint work with Masaaki Harada, S.Dougherty, and Manabu Oura). 3.I classified primitive symmetric association schemes with m_1=3 by using elementary geometric ideas such as the classifications of regular polyhedrons and quasi-regular polyhedrons. I am currently working on the classification of primitive symmetric Q-polynomial association schemes with m_1=4 jointly with Attila Sali.
アソシエーションスキームにおけるコードとデザイン

宗政昭弘, 笛田薫, 大塚寛, 柳川堯, 小西貞則, 坂内英一

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 一般研究(C)

Institution: 九州大学

1995 - 1995

More details Close

本研究ではアソシエーションスキームに付随した組合せ的構造と、統計的解析、およびそれらの応用を研究した。標数2の有限体上の二次形式のアソシエーションスキームを、交代形式のアソシエーションスキームと定義ベクトル空間との直積集合上に構成する方法を発見した。この方法により、一次元大きい交代形式のアソシエーションスキームも再構成できる他、新しいアソシエーションスキームが発見できる可能性が出てきた。また、研究分担者の坂内英一とともに、群アソシエーションスキームのTerwilliger代数の構造と、指標表から定まる群の不変量の関連を明らかにした。また坂内英一は、ハミングアソシエーションスキームの部分集合であるコードから、ヤコビ多項式をつくり、そこからさらにヤコビ形式が得られることを示した。さらに、研究分担者の柳川堯、笛田薫は、統計的検定問題を研究した。分割表に記述される多変量離散データの解析法を開発し、疎な分割表解析に関して、反応が非線形構造を持つ場合の検定を開発し、その漸近的性質について研究した。また、統計的検定問題において、観測標本の順位を対称群の元として扱うことにより対称群上の距離から導かれる順位検定統計量の性質を調べた。その結果、多くの距離から導かれる検定統計量は漸近正規性を持つことが示された。また、研究分担者の小西貞則は、現象解明のための有効な予測モデルの構築と、モデルの良さを測るための評価基準の構成を目的として研究を行った。さらに、大塚寛は、グラフを集合値関手圏とみなし、この上でグラフ変換のストリクト性の定式化と、それに基づく解析方法を与えた。
アソシェーションスキームとその双対性

宗政昭弘

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 奨励研究(A)

Institution: 九州大学

1994 - 1994

More details Close

有限アーベル群から単位元を除いた部分が1からtまでのt個のシフトとそれらの逆元の計2t個の元からなる部分集合にいつ分割できるかという問題をt=3.4のときに解決した。群の位数が素数べきの場合に帰着し、その素数の持つ数論的性質を用いて解を記述した。この問題がある種のコード理論に応用があることはLevenshtein-Vinckにより指摘されており、彼らはt=1,2のときの存在必要十分条件を得ていた。有限体上のベクトル空間の部分空間の族からなるブロックデザインについては、わずかなことしかわかっていない。本研究では、2元体または3元体上の7次元空間の3次元部分空間の族をうまく選ぶことにより新しいブロックデザインを構成した。この例は、現在知られている有限体上のブロックデザインの中で最小の会合数を持つものになっている。また、有限体上の6次元空間の場合には、自己同型群が点上可移に作用するようなブロックデザインの存在には非常に強い制約があることを示した。
代数的組合せ論の手法を用いるリンク、3次元多様体の位相不変量の構成

坂内悦子, 高田敏恵, 横田佳之, 宗政昭弘, 山田美枝子, 坂内英一

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 一般研究(C)

Institution: 九州大学

1994 - 1994

More details Close

スピンモデルが自己双対的アソシエーションスキームのボ-ズ・メスナ-代数と深く関係していることはF.Jaegerの仕事により知られていた。一方において自己双対的アソシエーションスキームのボ-ズ・メスナ-代数と共形場理論のフュージョン代数の間に関係があること、またその関連により、自己双対的アソシエーションスキームにもモジュラー不変性という概念が重要であることも坂内英一の研究により知られていた。この研究におていは、Hamming アソシエーションスキームのモジュラー不変性を完全に決定すると同時にスピンモデルが自己双対的アソシエーションスキームのモジュラー不変性と関連していることを発見した。さらに有限巡回群上のアソシエーションスキームのモジュラー不変性を完全に決定しその解から必ずしも対称でないスピンモデルを構成した。また有限巡回群上のアソシエーションスキームを対称化して得られるアソシエーションスキームのモジュラー不変性を完全に決定しさらに有限巡回群上のおよびその対称化のアソシエーションスキームのボ-ズ・メスナ-代数達を生成するスピンモデルを完全に分類した。これらの具体的な例の研究と同時に、スピンモデル、アソシエーションスキームの双対性およびモジュラー不変性の間の関係を深く研究して、ある種のアソシエーションスキームからスピンモデルを構成するアルゴリズムを見い出し、実際にそれを有限アーベル群に適用した、すなわち有限アーベル群上のアソシエーションスキームのモジュラー不変性を完全に決定し、必ずしも対称でないスピンモデルを構成した。さらに有限アベール群の双対性を分類することにより有限アーベル群のモジュラー不変性に付随するスピンモデルを完全に分類した。これらの研究の他にスピンモデルの定義をさらに一般化し4-ウエイトスピンモデルを定義した。
有限体上の二次形式及び交代形式の幾何学的研究

宗政昭弘

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 奨励研究(A)

Institution: 九州大学

1993 - 1993

More details Close

標数2の有限体上のベクトル空間上の二次形式全体の集合を距離正則グラフとみなしたときの全自己同型群を決定した。このとき、過去に知られていた自己同型群よりも実際の自己同型群の方が大きいことが判明した。従って全自己同型群の階数が偶数のとき、Witt indexが2種類でてくるが、この2種類はグラフの自己同型群では判定できないということがわかった。また、知られているP-and Q-polynomial association schemeの中で凸部分グラフの分類ができていない唯一の例が標数2の有限体上の2次形式のグラフであるが、この問題も完全に解決した。この結果は、自己同型群の決定と密接に関わりりあっている。自己同型群の決定の鍵となったのは、交代形式のグラフが二次形式のグラフの部分グラフとして含まれないという事実である。このことは二次形式のグラフの自己同型群の一点の安定部分群の決定を可能にしたばかりでなく、次元の小さい交代形式のグラフも二次形式のグラフの部分グラフでないことの証明の第一段階となった。
p進解析と代数的整数論

白谷克巳, 宗政昭弘, 山田美枝子, 坂内英一, 〓田英治, 末吉豊

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 一般研究(C)

Institution: 九州大学

1993 - 1993

More details Close

研究代表者白谷克巳は、p進L関数の研究から生ずるディリクレ指標のガウス和について、そのp進的な大ききの標価を研究し、ディリクレ指標の導手が奇素数のときグロス-コブリッツ公式の打ち切り合同式の簡明な証明を与え、更に一般に、導手が奇素数べきのときのガウス和のp進的大きさを精密に求めた。次に、ルビン-ティト形式群Fに付随するp進ゼーダ関数zetarho(s,F,h)のs=1での値を研究し、古典的に既知である種々の場合を含む統一的計算法を与えた。これらの結果は円分体の整数論への重要な応用をもつものである。末吉豊はルビン-ティト群の等分点の体でのノルム剰余記号を研究し、高木-白谷の公式の一般化を得た。吉田英治は、保型関数のスペクトル理論の中で、R-級数、H-級数を定義し、セルベルクの固有値予想に対し重要な道具になる得ることを示した。坂内英一、山田美枝子、宗政昭弘は、代数的組合せ論の方法を用いて、巡回群上のスピンモデルの構成と分類、アダマール行列の構成法、興味ある正則グラフの自己同型群などに新しい結果を得た。その他の研究分担者は、球面微分同相理論での多数の問題提起、極小曲面に近い曲面のガウス写像の擬等角度、(3,6)型超幾何微方程式のモノドロミイ群の生成元の決定、アレキサンドロフ空間の等長変換群などを研究し、興味ある諸結果を示した。
Study of association schemes

BANNAI Eiichi, YOSHIDA Masaaki, SHIRATANI Katsumi, INOUE Junko, MUNEMASA Akihiro, YAMADA Mieko

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for General Scientific Research (B)

Institution: KYUSHU UNIVERSITY

1992 - 1993

More details Close

The conceptof spin model was introduced by V.F.R.Jones in the paper published in Pac.J.Math. (1989). Each spin model gives a link invariant. The main research of the principal investigator in the last one year was in the following 2 directions. (1) Generalizing the concept of spin model and find such new spin models giving link invariants, (2) To study further spin models in connection with association schemes and releted object in algebraic combinatorics, then to study the construction and classfication problems of spin models in that framework. Explicit results are as follows. (1) In a joint work with Etsuko Bannai, we intriduced the concept of generalized generalized spin models (4-weighs spin models) by further generalizing the concept of generalized spin models introduced by Kawagoe-Munemasa-Watatani. We also constructed spin models on finitte cyclic groups by using the classification of the modular invariance properties on finite cyclic groups. (2) In a jouint work with Etsuko Bannai and F.Jaeger, we proved that the modular invariance holds if a generalized spin model generates the Bose-Mesner algebra of an association scheme, and we classified the modular invariance properties on finite abelian groups. We also proved that each such solution of the modular invariance gives a spin model on the abelian group, which generalizes the work of Kac and Wakimoto of the construction of spin models on abelian groups from an even Q-form. We also obtained the classification of small spin models in a joint work with F.Jaeger and A.Sali.
差集合とassociation schemeの関連性の研究

山田美枝子, 宗政昭弘, 末吉豊, 三町勝久, 坂内英一, 白谷克巳

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 一般研究(C)

Institution: 九州大学

1992 - 1992

More details Close

差集合およびHadamard行列とassociation schemeの間の関係は、これまでは一般論として論じられていたが、研究代表者はZ/4Zの拡大環上で、amorphous association schemeが存在し、それとHadamard差集合との関係を明らかにして、これらの間の具体的な関係を示した。最近になってHadamard行列、association schemeがspin modelを通して、linkの不変量に関係することが明らかになった。最初にspin modelからlinkの不変量が求まることを示したのはJonesである。このspin modelの概念は宗政-綿谷(北大)により非対称な場合に拡張されたが、坂内はこの概念をさらに拡張した。すなわち、4つの正方行列でいくつかの条件をみたすものを拡張したspin modelと呼び、新しいlinkの不変量が得られる可能性を示した。4つの行列のうち2つが等しいとき、宗政-綿谷によるspin modelにさらに対称であるとき Jonesによるものに一致する。拡張したspin modelの中でHadamard行列に関係するものを特にHadamard型と名づけた。この場合のspin modelを与えるHadamard行列は正則である。1985年にA.A.Ivanor-I.V.Chuvaeraにより4n次Hadamard行列から、クラス4のamorphous association schemeが得られることが証明された。さらにこのassociation schemeから16n^2次正則Hadamard行列、Hadamard差集合が得られる。これを使って、もとのHadamard行列がHadamard行列のある同値類に含まれていれば amorphous association schemeを通して得られるHadamard行列はspin modelとなることが証明できた。以上のように本研究で、Hadamard差集合とassociation schemeの関係をspin modelを構成するという立場から考えるという新しい視点を得た。この研究を今後も進展させたい。
代数的組合せ論国際会議へ向けての準備

坂内英一, 川中宣明, 伊藤達郎, 野村和正, 宗政昭弘, 山田美枝子

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 総合研究(B)

Institution: 九州大学

1992 - 1992

More details Close

1.アソシエーションスキームを用いてのスピンモデルの研究に特に著しい進展を見た。(1)スピンモデルの概念の一般化、(2)スピンモデルの新しい例の構成、(3)アソシエーションスキームとスピンモデルの間のより深い関係の発見、などがこの一年間に得られた最大の成果である。 (1)Jonesにより1989年に導入されたスピンモデルの概念は、先ず宗政-綿谷により(非対称性を許す)generalized spin modelの導入という形で、拡張され、次に坂内英一-坂内悦子によりスピンモデルの最終版ともいえるgeneralized generalized spin modelの概念に態達態に到達した。 (2)先ず、坂内-坂内によるHamming association snhemeの指標表における modular invariance の発見と、それを用いての坂内-坂内-生田-生越によるHamming association scheme 上のスピンモデルの構成に始まった。これは野村和正によるHadamardグラフのスピンモデルの構造、坂内-坂内による巡回群上のスピンモデルのfamily 構成につながった。またこれは脇本実によるLie環から出来るspin models の構成を導いた。またHadamard 行列と関連した色々の新しい形のスピンモデルも山田実校子により構造された。 (3)坂内-坂内-Jaegerによるスピンモデルの存在とmodular invarianceの関係の明確化、坂内-Jaeger-Saliによる小さなsizeのスピンモデルの決定などの成果が得られた。 2.この総合Bによる援助のため、代数的組合せ論国際会議の準備は著しく進展し、平成5年11月22-26日に九大において“Algebraic Combinatorice(Fukuoka,1993)"の開催計画を文部省に提案していたが、このたび、内定を受けた。現在、その開催の準備に全力をあげて努力している所である。

Show all Show first 5

Teaching Experience 1

Discrete Mathematics　Tohoku University

Other 2

距離正則グラフと球面上のデザイン

More details Close

距離正則グラフの球面上への表現と、関連するグラフのスペクトルについての代数的研究を通じて日韓の研究者の交流を促進する。
距離正則グラフとその周辺

More details Close

距離正則グラフと関連する組合せ構造についての代数的研究を通じて日韓の研究者の交流を促進する。