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

• 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
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,820,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥420,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 対称横断デザイン / 有限射影平面 / 有限幾何学 / 横断デザイン / 自己同型群 / 結合構造 / 結合行列 / 群環 / 有機幾何学

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 projective planes of order 12 with a collineationgroup of order 9 (2009)
  • Author(s): K. Akiyama, C. 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] A contraction of square transversal designs (2008)
  • Author(s): Y. Hiramine, C. Suetake
  • Journal Title: Discrete Mathematics 308 Pages: 3257-3264
  • Peer Reviewed
• [Journal Article] On STDk/3[k ; 3]'s (2008)
  • Author(s): K. Akiyama C. 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): K. Akiyama, C. Suetake
  • Journal Title: Journal of combinatorial designs 16 Pages: 411-430
  • 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] On blocking semiovals with an 8-secant in projective planes of order 9 (2006)
  • Author(s): Nobuo Nakagawa, Chihiro Suetake
  • Journal Title: Hokkaido Mathematical Journal 35・2 Pages: 137-156
• [Journal Article] A contraction of divisible designs (2006)
  • Author(s): Yutaka Hiramine, Chihiro Suetake
  • Journal Title: Algebraic Combinatorics (An International Conference in Honor of Eiichi Bannai's 60^<th> Birthday) Pages: 146-150
• [Journal Article] 対称横断デザインにおける軌道定理 (2006)
  • Author(s): 末竹 千博
  • Journal Title: 研究集会「デザイン理論とその周辺」報告集 Pages: 99-106
• [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
  • Peer Reviewed
• [Journal Article] On STDk/3[k;3]'s
  • Author(s): K. Akiyama, C. Suetake
  • Journal Title: Discrete Mathematicsから出版予定
  • Peer Reviewed
• [Journal Article] A contraction of square transversal designs
  • Author(s): Y. Hiramine, C. Suetake
  • Journal Title: Discrete Mathematicsから出版予定
  • Peer Reviewed
• [Journal Article] The nonexistence of projective planes of order 12 with a collineation group of order 8
  • Author(s): K. Akiyama, C. Suetake
  • Journal Title: Journal of combinatorial designsから出版予定
  • 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] On projective planes of order 12 with a collineation group of order 9 (2008)
  • Author(s): 秋山献之, 末竹千博
  • Organizer: 第25回代数的組合せ論
  • Place of Presentation: 北海道大学
  • Year and Date: 2008-06-25
• [Presentation] The nonexistence of STD2[12 ; 6]'s with an automorphism group of order 9 (2008)
  • Author(s): 末竹千博
  • Organizer: 第25回代数的組合せ論
  • 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] STD2{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] Automorphism groups of a symmetric transversal design STD_2[12;6] (2007)
  • Author(s): 末竹千博
  • Organizer: International Conference on Advances in Interdisc-iplinary Statistics and Combinatorics
  • Place of Presentation: ノースカロライナ大学(米国)
  • 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] The nonexistence of projective planes of order 12 with a collineation Group of order 8 (2007)
  • Author(s): 秋山献之, 末竹千博
  • Organizer: 第24回代数的組合せ論研究集会
  • 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] Automorphism groups of a symmetric transversal design STD_2[12;6] (2007)
  • Author(s): 末竹千博
  • Organizer: International Workshop on Combinatrics 2007
  • Place of Presentation: 慶応義塾大学
  • 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