Finite projective planes, GL-semiregular STD, and LO-semiregular STD

2008 Fiscal Year Final Research Report

• Project/Area Number: 18540132
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Oita University
• Principal Investigator: SUETAKE Chihiro Oita University, 工学部, 教授 (80353241)
• Project Period (FY): 2006 – 2008
• Keywords: 対称横断デザイン / 有限射影平面 / 有限幾何学

Research Abstract

elation群を使って, 対称横断デザインを縮小する方法をつくった。この方法を使って, STD_2[12 ; 6]が非自明なelationを持たないことを示した。クラスサイズ3のGL正則STDの分類をブロックサイズ18までした。位数12の射影平面が位数8の自己同型群を持たないことと, 位数9の巡回自己同型群を持たないことを示した。

Research Products

• [Journal Article] On projective planes of order 12 with a collineation group of order 9 (2009)
  • Author(s): Kenzi Akiyama and Chihiro Suetake
  • Journal Title: Australasian Journal of Combinatorics 43 Pages: 133-162
  • Peer Reviewed
• [Journal Article] On STD_k/3[k ; 3]'s (2008)
  • Author(s): Kenzi Akiyama and Chihiro Suetake
  • Journal Title: Discrete Mathematics 308 Pages: 6449-6465
  • Peer Reviewed
• [Journal Article] The nonexistence of projective planes of order 12 with a collineation group of order 8 (2008)
  • Author(s): Kenzi Akiyama and Chihiro Suetake
  • Journal Title: Journal of Combinatorial Designs 16 Pages: 411-430
  • Peer Reviewed
• [Journal Article] A contraction of square transversal designs (2008)
  • Author(s): Yutaka Hiramine and Chihiro Suetake
  • Journal Title: Discrete Mathematics 308 Pages: 3257-3264
  • Peer Reviewed
• [Journal Article] On blocking semiovals with an 8-secant in projective planes of order 9 (2006)
  • Author(s): Chihiro Suetake and Nobuo Nakagawa
  • Journal Title: Hokkaido Mathematical Journal 35 Pages: 437-456
  • Peer Reviewed
• [Journal Article] Automorphism group of a symmetric tranversal design STD_2[12 ; 6]
  • Author(s): Chihiro Suetake
  • Journal Title: Journal of Statistical Theory an Practice Pages: 17(掲載予定)
  • Peer Reviewed
• [Presentation] The nonexistence of STD_2[12 ; 6]'s (2008)
  • Author(s): 末竹千博
  • Organizer: with an automorphism group of order 9
  • Place of Presentation: 北海道大学
  • Year and Date: 2008-06-25
• [Presentation] STD_2[12;6]'sの自己同型群について (2008)
  • Author(s): 末竹千博
  • Organizer: 代数的組合せ論とその周辺
  • Place of Presentation: 崇城大学
  • Year and Date: 2008-05-10
• [Presentation] 位数12の射影平面について (2008)
  • Author(s): 末竹千博
  • Organizer: 第118回日本数学会九州支部例会
  • Place of Presentation: 琉球大学
  • Year and Date: 2008-02-02
• [Presentation] Automorphism group of a symetric transversal design STD_2[12 ; 6] (2007)
  • Author(s): 末竹千博
  • Organizer: International Conference on Advances in Interdisciplinary Statistics and Combinatorics
  • Place of Presentation: The University of North Carolina at Greensboro, USA
  • Year and Date: 2007-10-12
• [Presentation] The nonexistence of projective planes of order 12 with a collineation group of order 8 (2007)
  • Author(s): 末竹千博
  • Organizer: 第24回代数的組合せ論
  • Place of Presentation: 近畿大学
  • Year and Date: 2007-06-30
• [Presentation] Automorphism groups of a symmetric transversal design STD_2[12 ; 3] (2007)
  • Author(s): 末竹千博
  • Organizer: International Workshop on Combinatorics 2007(Keio Sessions)
  • Place of Presentation: 慶応大学
  • Year and Date: 2007-06-08
• [Presentation] 対称横断デザインにおける軌道定理 (2006)
  • Author(s): 末竹千博
  • Organizer: デザイン理論とその周辺
  • Place of Presentation: 上山市「日本の宿古窯」
  • Year and Date: 2006-11-12
• [Presentation] A contraction ofdivisible designs (2006)
  • Author(s): 末竹千博
  • Organizer: Algebraic Combinatorics(An International Conference in Hinor of Eiichi Bannai's 60^<th> Birthday)
  • Place of Presentation: 仙台国際センター
  • Year and Date: 2006-07-27