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Association schemes and spin models

Research Project

Project/Area Number 10440011
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKYUSHU UNIVERSITY

Principal Investigator

BANNNAI Etsuko  Kyushu Univ., Graduate School of Math., Assoc. Professor, 大学院・数理研究院, 助教授 (00253394)

Co-Investigator(Kenkyū-buntansha) ITO Tatsuro  Kanazawa Univ., Faculty of Science, Professor, 理学部, 教授 (90015909)
MUNEMASA Akihiro  Kyushu Univ., Graduate School of Math., Assoc. Professor, 大学院・数理研究院, 助教授 (50219862)
BANNAI Etsuko  Kyushu Univ., Graduate School of Math., Professor, 大学院・数理研究院, 教授 (10011652)
NOMURA Kazumasa  Tokyo Medical and Dental Univ., Faculty of Cultural Science, Professor, 教養部, 教授 (40111645)
Project Period (FY) 1998 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥5,300,000 (Direct Cost: ¥5,300,000)
Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2000: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1999: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsSpin model / Association Schemes / designs / Bose-Mesnsr algebra / type II matrices / s-distance sets / modular invariance / 4-weight spin models / typeII行列 / 代数的組合せ論 / self dual / symmetric design / SDP / 自己双対性
Research Abstract

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.

Report

(5 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (93 results)

All Other

All Publications (93 results)

  • [Publications] E.Bannai, A.Munemasa: "Duality maps of finite abelian groups and their application to spin models"J. of Algebraic Combinatorics. 8. 223-233 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E.Bannai, E.Bannai, M.Ozeki, Y.Teranishi: "On the ring of simultaneous invariants for the Gleason-MacWilliams group"Europ. J. Combinatorics. 20. 619-627 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E.Bannai, M.Sawano: "The classification of certain four-weight spin models"Annals of Combinatorics. 4. 139-151 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E.Bannai: "Bose-Mesner Algebras Associated with Four-weight Spin Models"Graphs and Combinatorics. 17. 589-598 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E.Bannai, M.Sawano: "Symmetric Designs Attached to Four-Weight Spin Models"Designs, Codes and Cryptography. 25. 73-90 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E.Bannai: "Modular invariance property of association schemes, Type II codes over finite rings and finite abelian groups, and reminscences of Francois Jaeger(a survey)"Ann. Inst. Fourier. 49. 763-782 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E.Bannai, S.T.Dougherty, M.Harada, M.Oura: "Type II codes, even unimodular lattices and invariant rings"IEEE Trans. Inform. Theory. 45. 1194-1205 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E.Bannai: "An introduction to association schemes"Methods of discrete mathematics (Braunschweig, 1999) Quad. Mat., 5, Aracne, Rome. 5. 1-70 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E.Bannai, M.Koike, A.Munemasa, J Sekiguchi: "Some Results on Modular Forms,-Subgroups of the Modular Group Whose Ring of Modular Forms is a Polynomial Ring"Advanced Studies in Pure Mathematics. 32. 245-254 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Kitazume, A.Munemasa: "New 5-designs with automorphism group PSL(2,23)"J. Combin. Des.. 7. 147-155 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Munemasa: "Flag-transitive 2-designs arising from line-spreads in PG(2n-1,2)"Geom. Dedicata. 77. 209-213 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] K.Betsumiya, M.Harada, A.Munemasa: "Type II codes over F_<2r>""Applied Algebra, Algebraic Algorithms and Error Correcting Codes," Springer Lecture Notes in Comp. Sci. 2227. 102-111 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A.Munemasa: "A mass formula for Type II codes over finite fields of characteristic two"The Ohio State University Mathematical Research Institute Monograph Series. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Harada, A.Munemasa: "A quasi-symmetric 2-(49,9,6) design"J. Combin. Des.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] S.Hobart, T.Ito: "The structure of nonthin irreducible T-modules of endpoint 1: ladder bases and classical parameters"J. Algebraic Combinatorics. 7. 53-75 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Ishibashi, T.Ito, M.Yamada: "Terwilliger Algebras of Cyclotomic Schemes and Jacobi Sums"Europ. J. Combinatorics. 20. 397-410 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Ito, K.Tanabe, P.Terwilliger: "Some algebra related to P-and Q-polynomial association schemes"DIMACS Series in Discrete Mathematics and Theoretical Computer Science. 56. 167-192 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] F.Jaeger, M.Matsumoto, K.Nomura: "Bose-Mesner algebras related with type II matrices and spin models"J. Alg. Combin.. 8. 39-72 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] K.Nomura: "Type II matrices of size five"Graphs Combin.. 15. 79-92 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] F.Jaeger, K.Nomura: "Symmetric versus Non-symmetric spin models for link invariants"J. Alg. Combin.. 10. 241-278 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Ikuta, K.Nomura: "General form of non-symmetric spin models"J. Alg. Combin.. 12. 59-72 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] K.Nomura: "A property of solusions of modular invariance equations for distance-regular graphs"Kyushu J. Math.. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 坂内英一, 坂内悦子: "球面上の代数的組合せ理論"シュプリンガー東京. xvi+367 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E. Bannai and A. Munemasa: "Duality maps of finite abelian groups and their application to spin models"J. of Algebraic Combinatorics. 8. 223-233 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E. Bannai and E Bannai: "Algebraic Combinatorics on spheres,(in Japanese)"Springer Tokyo. xvi+367 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E. Bannai and M. Sawano: "The classification of certain four-weight spin models"Annals of Combinatorics. 4. 139-151 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E. Bannai: "Bose-Mesner Algebras Associated with Four-weight Spin Models"Graphs and Combinatorics. 17. 589-598 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E. Bannai and M. Sawano: "Symmetric Designs Attached to Four-Weight Spin Models"Designs, Codes and Cryptography. 25. 73-90 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E. Bannai, E Bannai, M. Ozeki and Y. Teranishi: "On the ring of simultaneous invariants for the Gleason-MacWilliams group"Europ. J. Combinatorics. 20. 619-627 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E. Bannai: "Modular invariance property of association schemes, Type II codes over finite rings and finite abelian groups, and reminiscences of Francois Jaeger(a survey)"Ann. Inst. Fourier. 49. 763-782 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E. Bannai, S. T. Dougherty, M. Harada and M. Oura: "Type II codes, even unimodular lattices and invariant rings"IEEE Trans. Inform. Theory. 45. 1194-1205 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E. Bannai: "An introduction to association schemes"Methods of discrete mathematics (Braunschweig, 1999) Quad. Mat., 5, Aracne, Rome. 1-70 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] E. Bannai, M. Koike, A. Munemasa, Akihiro and J Sekiguchi: "Some Results on Modular Forms, - Subgroups of the Modular Group Whose Ring of Modular Forms is a Polynomial Ring"Advanced Studies in Pure Mathematics. Vol 32. 245-254 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Kitazume and A. Munemasa: "New 5-designs with automorphism group PSL(2, 23)"J. Combin. Des.. 7. 147-155 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Munemasa: "Flag-transitive 2-designs arising from line-spreads in PG(2n - 1, 2)"Geom. Dedicata. 77. 209-213 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] K.Betsumiya. M. Harada and A. Munemasa: "Type II codes over F_2^r, "Applied Algebra, Algebraic Algorithms and Error Correcting Codes""Springer Lecture Notes in Comp. Sci. 2227. 102-111 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] A. Munemasa: "A mass formula for Type II codes over finite fields of characteristic two"The Ohio State University Mathematical Research Institute Monograph Series. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Harada and A. Munemasa: "A quasi-symmetric 2-(49,9,6) design"J. Combin. Des. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] S. Hobart and T. Ito: "The structure of nonthin irreducible T-modules of endpoint 1 : ladder bases and classical parameters"J. Algebraic Combinatorics. 7. 53-75 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Ishibashi, T. Ito and M. Yamada: "Terwilliger Algebras of Cyclotomic / Schemes and Jacobi Sums"Europ. J. Combinatorics. 20. 397-410 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Ito, K. Tanabe, P. Terwilliger: "Some algebra related to P- and Q-polynomial association schemes"DIMACS Series in Discrete Mathematics and Theoretical Computer Science. 56. 167-192 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] F. Jacger, M. Matsumoto and K. Nomura: "Bose-Mesner algebras related with type II matrices and spin models"J. Alg. Combin.. 8. 39-72 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] K. Nomura: "Type II matrices of size five"Graphs Combin.. 15. 79-92 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] F. Jaeger and K. Nomura: "Symmetric versus Non-symmetric spin models for link invariants"J. Alg. Combin.. 10. 241-278 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Ikuta and K. Nomura: "General form of non-symmetric spin models"J. Alg. Combin.. 12. 59-72 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] K. Nomura: "A property of solution of modular invariance equations for distance-regular graphs"Kyushu J. Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Etsuko Bannai: "Bose-Mesner Algebras Associated with Four-weight spin models"Graphs and Combinatorics. 17. 589-598 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Etsuko Bannai, Mitsuhiro Sawano: "Symmetric Designs Attached to Four-weight Spin Models"Designs, Codes and Cryptography. 25. 73-90 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] K.Nomura, B.Curtin: "Spin models and strongly hyper-self-dual Bose-Mesner algebras"J.Alg.Combin. 13. 173-186 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] K.Nomura: "A property of solutions of modular in variance equations for distance-regular graphs"Kyushu-J.Math. (発表予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] E.Bannai, M.Koike, A.Munemasa, J.Sekiguchi: "Some results on modular forms"Advan-ced Studies in Pure Mathematics. 32. 245-254 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] A.Munemasa, K.Betsumiya, M.Harada: "Type II codes over F_2r"Springer Lecture Notes in Comp.Sci.(Applied Alg. Algebraic, Algorithm and Error …. 2227. 102-111 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Etsuko Bannai (with M.Sawano): "The classification of certain four-weight spin models"Annals of Combin.. 4. 139-151 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Etsuko Bannai: "Bose-Mesner algebras associated with four-weight spin models"Graphs and Combin.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Eiichi Bannai et.al: "Some Results on Modular Forms-Subgroups of the Modular Group Whose Ring of Modular Forms is a Polynomial Ring"Advanced Studies in Pure Mathematics, to appear. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Akihiro Munemasa (with M.Harada): "Classification of Type IV Self-Dual Z_4-Codes of Length 16"Finite Fields and Their Applications. 6. 244-254 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Akihiro Munemasa: "A Mass Formula for Type II Codesover Finite Fields of Characteristic Two"The Ohio State University Mathematical Research Institute Monograph Series.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Tatsuro Ito (with K.Tanabe,P.Terwilliger): "Some algebra related to P- and Q-polynomial association schemes"DIMACS : Series in Discrete Mathematics and Theoretical Computer Science/BARG. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Kazumasa Nomura (with A.Hiraki,H.Suzuki): "Distance-regular graphs of valency 6 and α_1=1"J.Alg.Combin.. 11. 101-134 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kazumasa Nomura (with B.Curtin): "Distance-regular graphs related to the quantum enveloping algebra sl (2)"J.Alg.Combin.. 12. 25-36 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kazumasa Nomoura (with T.Ikuta): "General form of non-symmetric spin models"J.Alg.Combin.. 12. 59-72 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kazumasa Nomura (with B.Curtin): "Spin models and strongly hyper-self-dual Bose-Mesner algebras"J.Alg.Combin.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Kazumasa Nomura: "A property of solusions of modular invariance equations for distance-regular graphs"Kyushu J.Math..

    • Related Report
      2000 Annual Research Report
  • [Publications] Etsuko Bannai: "Bose-Mesner algebras associated with four-weight spin models"Graphs and Combinatorics.

    • Related Report
      1999 Annual Research Report
  • [Publications] Ei. Bannai, Et. Bannai, Michio Ozeki and Yasuo Teranishi: Europ. J. Combinatorics. 20. 619-627 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Eiichi Bannai: "Modular invariance property of association schemes, Type II codes over finite rings and finite abelian groups, and reminscences of Francois Jaeger(a survey),"Ann. Inst. Fourier. 49. 763-782 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Ei. Bannai, S. T. Dougherty, M. Harada and M. Oura: "Type II codes, even unimodular lattices and invariant rings"IEEE Trans. Inform. Theory. 45. 1194-1205 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] A. Munemasa and M. Kitazume: "New 5-designs with automorphism group PSL(2,23),"J. Combinatorial Designs. 7. 147-155 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] A. Munemasa and J. H. Koolen: "Tight 2-designs and perfect 1-codes in Doob graphs"J. Stat. Planning and Inference. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Akihiro Munemasa: "Flag-transitive 2-designs arising from line-spreads in PG(2n-1,2)"Geometriae Dedicata. 77. 209-213 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] A. Munemasa S. T. Dougherty, P. Gaborit, M. Harada and P. Sole: "Type IV Self-Dual Codes over Rings"IEEE Trans. Inform. Theory. 45. 2345-2360 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H. Ishibashi, T. Ito and M. Yamada: "Terwilliger Algebras of Cyclotomic Schemes and Jacobi Sums"Europ. J. Combinatorics. 20. 397-410 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Kazumasa Nomura: "Type II matrices of size five"Graphs and Combin. 15. 79-92 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] K. Nomura and F. Jaeger: "Symmetric versus Non-symmetric spin models for link invariants"J. Alg. Combin. 10. 241-278 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] K. Nomura and B. Curtin: "Some formulas for spin models on distance-regular graphs"J. Combin. Theory(B). 75. 206-236 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Kazumasa Nomura: "Spin Models and Bose-Mesner Algebras"Europ. J. Combin.. 20. 691-700 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] K. Nomura and T. Ikuta: "General form of non-symmetric spin models"J. Alg. Combin.,. (to appear.).

    • Related Report
      1999 Annual Research Report
  • [Publications] Ei. Bannai, Et. Bannai, Michio Ozeki and Yasuo Teranishi: "On the ring of simultaneous invariants for the Gleason-Mac Williams group,"Europ. J. Combinatorics. 20. 619-627 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 坂内英一・坂内悦子: "球面上の代数的組合せ理論"シュプリンガーフェアラーク東京. xvi+367 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 坂内悦子: "Duality maps of finite abelian groups and their applications to spin models(with Akihiro.Munemasa)" J.Algebraic Combinatorics. 8. 223-233 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 坂内英一: "On the ring of simultaneous invariants for the Gleason-MacWilliams group(with Etsuko Bannai,Michio Ozeki and Yasuo Teranishi)" accepted for publication,European J.Combinatorics.

    • Related Report
      1998 Annual Research Report
  • [Publications] 坂内英一: "Modular invariance property of association schemes,Type II codes over finite rings and finite abelian groups,and reminscences of Francois Jaeger(a survey)" Ann.Inst.Fourier,Grenoble. 49(accepted for publication.). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 坂内英一: "Type II codes,even unimodular lattices and invariant rings(with Steven T.Dougherty,Masaki Harada and Manabu Oura)" IEEE Trans.Information Theory. (accepted for publication).

    • Related Report
      1998 Annual Research Report
  • [Publications] 宗政昭弘: "Orthogonal arrays,primitive trinomials,and shift-register sequences" Finite Fields and Their Applications. 4. 252-260 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 宗政昭弘: "New 5-designs with aoutomorphism group PSL(2,23)" J.Combinatorial Designs(with M.Kitazume). (accepted for publication.).

    • Related Report
      1998 Annual Research Report
  • [Publications] 宗政昭弘: "Tight 2-designs and perfect 1-codes in Doob graphs" J.Stat.Planning and Inference(with J.H.Koolen). (accepted for publication.).

    • Related Report
      1998 Annual Research Report
  • [Publications] 宗政昭弘: "Flag-transitive 2-designs arising from line-dpreads in PG(2n-1,2)" Geometriae Dedicate. (accepted for publication).

    • Related Report
      1998 Annual Research Report
  • [Publications] 伊藤達郎: "The structure of nonthin irreducible T-modules of endpoint 1:ladder bases and classical parameters(Sylvia Hobart)" Journal of Algebraic Combinatorics. 7. 53-75 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 伊藤達郎: "Terwilliger algebras of cyclotomic schemes and Jacobi sums(Haruo Ishibashi,Mieko Yamada)" European Journal of Combinatorics. (accepted for publication).

    • Related Report
      1998 Annual Research Report
  • [Publications] 野村和正: "Bose-Mesner algebras related to type II matrices and spin models(with F.Jaeger and M.Matsumoto)" J.Algebraic Combinatorics. 8. 39-72 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 野村和正: "Type II matrices of size five" Graphs and Combinatorics. (accepted for publication).

    • Related Report
      1998 Annual Research Report
  • [Publications] 野村和正: "Symmetric versus Non-symmetric spin models for link invariants(with F.Jaeger)" J.Algebraic Combinatorics. (accepted for publication).

    • Related Report
      1998 Annual Research Report
  • [Publications] 野村和正: "Some formulas for spin models on distance-regular graphs(with B.Curtin)" J.Combinatorial Theory(B). (accepted for publication).

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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