Conclusive study of algebraic combinatorics

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20540017
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyushu 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

• [Journal Article] Toy models for D.H.Lehmer's conjecture (2010)
  • 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-figurations (2010)
  • 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 spheres (2009)
  • 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 designs (2010)
  • 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^n (2010)
  • 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 theory (2010)
  • 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 conjecture (2010)
  • 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 designs (2009)
  • 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 conjecture (2009)
  • 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 configurations (2009)
  • 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