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2010 Fiscal Year Self-evaluation Report

Conclusive study of algebraic combinatorics

Research Project

  • PDF
Project/Area Number 20540017
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKyushu University

Principal Investigator

BANNAI Eiichi  Kyushu University, 大学院・数理学研究院, 学術研究者 (10011652)

Project Period (FY) 2008 – 2012
Keywords代数的組合せ論 / アソシエーションスキーム / モジュラー形式 / デザイン / tightデザイン / 格子 / コード / Lehmer予想
Research Abstract

代表者の長年の代数的組合せ論の研究の総決算を行うと言う形で,いままでの研究の総まとめをしたいと言うのがこの研究の主旨である.置換群の多重可移という性質と,原始的であると言う性質の意味をもっと良く理解したいということが研究の元々の出発点であったが,それをより広げた形で,アソシエーションスキーム,あるいは球面上の代数的組合せ論と言う枠組みで,アソシエーションスキーム上の,あるいは球面上のt-デザインにおけるtの意味を良く理解したいと言うことであった.具体的には,アソシエーションスキーム自身の分類問題に加えて,アソシエーションスキームの部分集合である,コード,デザインの研究を行い,さらに球面上の良い有限集合の研究,およびその拡張であるユークリッドデザイン等の研究を行った.特に,ユークリッド格子の殻として出来る球面t-デザインの研究(Lehmer予想のtoy modelsの研究),ユークリッドデザインとcoherent configurationとの関係の研究,特にtightなユークリッドt-デザインの構成,分類問題に努力を集中して研究を行った

  • Research Products

    (13 results)

All 2010 2009 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (7 results)

  • [Journal Article] Toy models for D.H.Lehmer's conjecture2010

    • Author(s)
      Eiichi Bannai, Tsuyoshi Miezaki
    • Journal Title

      J.of Math.Soc.Japan 62

      Pages: 687-705

    • Peer Reviewed
  • [Journal Article] Euclidean designs and coherent con-figurations2010

    • Author(s)
      Eiichi Bannai, Etsuko Bannai
    • Journal Title

      Contemporary Mathematics(ed.Richard Brualdi) (American Math.Soc.) 531

      Pages: 59-93

    • Peer Reviewed
  • [Journal Article] 純粋数学としての組合せ論2010

    • Author(s)
      坂内英一
    • Journal Title

      数学 62

      Pages: 433-452

    • Peer Reviewed
  • [Journal Article] A survey on spherical designs and algebraic Combinatorics on spheres2009

    • Author(s)
      Eiichi Bannai, Etsuko Bannai
    • Journal Title

      Europ.J.Combinatorics 30

      Pages: 1392-1425

    • Peer Reviewed
  • [Journal Article] Tight 9-designs on two concentric spheres

    • Author(s)
      Eiichi Bannai, Etsuko Bannai
    • Journal Title

      J.of Math.Soc.Japan 印刷中

    • Peer Reviewed
  • [Journal Article] A new example of Euclidean tight 6-design

    • Author(s)
      Eiichi Bannai, Etsuko Bannai, Junichi Shigezumi
    • Journal Title

      Annals of Combinatorics 印刷中

    • Peer Reviewed
  • [Presentation] A survey on spherical designs and Euclidean designs2010

    • Author(s)
      Eiichi Bannai
    • Organizer
      Geometry, Topology, Algebra and Number Theory,Applications (Delone-120Conference)
    • Place of Presentation
      Steklov Math.Inst., Moscow, Russia(plenary talk)
    • Year and Date
      20100816-20100820
  • [Presentation] Euclidean designs and cubature formulas for spherical symmetric measures on R^n2010

    • Author(s)
      Eiichi Bannai
    • Organizer
      Optimal Configurations on the Sphere and Other Manifolds
    • Place of Presentation
      Vanderbilt Univ, Nashville, USA(30 min)
    • Year and Date
      2010-05-19
  • [Presentation] Spherical designs and toy models for D.H.Lehmer's conjecture in number theory2010

    • Author(s)
      Eiichi Bannai
    • Organizer
      University of Rome 1 (La Sapienza)
    • Place of Presentation
      (60 min.)
    • Year and Date
      2010-04-22
  • [Presentation] Spherical designs and D.H.Lehmer's conjecture2010

    • Author(s)
      Eiichi Bannai
    • Organizer
      Focused Week on Integral Lattices, University of Florida
    • Place of Presentation
      Gainesville, Florida, USA.(50 minutes)
    • Year and Date
      2010-02-16
  • [Presentation] Review of spherical designs2009

    • Author(s)
      Eiichi Bannai
    • Organizer
      CIMPA-UNESCO-PHILIPPINES School : Semidefinite Programming in Algebraic Com-binatorics
    • Place of Presentation
      University of the Philippines, Manilla(five 50 minute talks)
    • Year and Date
      20090720-20090731
  • [Presentation] Toy models of D.H.Lehmer's conjecture2009

    • Author(s)
      Eiichi Bannai
    • Organizer
      The analytic theory of modular forms at the 65th birthday of Roelof Bruggeman
    • Place of Presentation
      Woudschoten, The Netherlands(60 minutes)
    • Year and Date
      2009-06-18
  • [Presentation] Spherical designs and association schemes versus Euclidean designs and coherent configurations2009

    • Author(s)
      Eiichi Bannai
    • Organizer
      IPM-International Workshop on Combinatorics 2009
    • Place of Presentation
      IPM, Tehran, Iran(60 minutes)
    • Year and Date
      2009-05-16

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Published: 2012-02-13   Modified: 2016-04-21  

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