Finite projective planes and symmetric divisible designs

• Project/Area Number: 21540139
• 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 大分大学, 工学部, 教授 (80353241)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 対称横断デザイン / 対称分割デザイン / 一般アダマール行列 / 有限射影平面 / 自己同型群 / クラス正則対称横断デザイン / 結合行列 / 群環

Research Abstract

We proved that the order of an automorphism group of any symmetric transversal design STD_2[12 ; 6] is 2^α3^β for some nonnegative integers α and β. We proved that ifπis a projective plane of order 12 admitting a collineation group G of order 9, then G is an elementary abelian group andπis not planar. We classified STD_6[18 ; 3]'s and STD_7[21 ; 3]'s that have a semiregular nonisomorphic automorphism group of order 9 on both points and blocks containing an elation of order 3. We showed that the number of nonisomorphic STD_8[24 ; 3]'s is at least 24.

Research Products

• [Journal Article] On symmetric transversal designs STD_8[24 ; 3]'s (2010)
  • Author(s): Teppei Hatono and Chihiro Suetake
  • Journal Title: International Journal of Combinatrics Volume: 2010 Pages: 14-14
• [Journal Article] On symmetric transversal designs STD_8[24;3]'s (2010)
  • Author(s): T.Hatono, C.Suetake
  • Journal Title: International journal of Combinatorics Volume: V2010 Pages: 1-14
  • Peer Reviewed
• [Journal Article] On STD_6[18, 3]'s and STD_7[21, 3]'s admitting a semiregular automorphism group of order 9 (2009)
  • Author(s): Kenzi Akiyama, Masayuki Ogawa, and Chihiro Suetake
  • Journal Title: Electron. J. Combin Volume: 16 Pages: 21-21
  • Peer Reviewed
• [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: Australas. J. Combin Volume: 43 Pages: 133-162
  • Peer Reviewed
• [Journal Article] Automorphism group of a symmetric transversal design STD_2[12 ; 6] (2009)
  • Author(s): Chihiro Suetake
  • Journal Title: Journal of Statistical Theory and Practice 3 Volume: No.2 Pages: 429-443
  • Peer Reviewed
• [Journal Article] Automorphism groups of a symmetric transversal design STD_2[12;6] (2009)
  • Author(s): C.Suetake
  • Journal Title: Journal of statistical theory and practice 3 Pages: 429-443
  • Peer Reviewed
• [Journal Article] On STD_6[18,3]'s and STD_7[21,3]'s admitting a semiregular Automorphism group of order 9 (2009)
  • Author(s): K.Akiyama, M.Ogawa, C.Suetake
  • Journal Title: The electronic journal of combinatorics 16
  • Peer Reviewed
• [Presentation] 捩れ巡回型一般アダマール行列 (2011)
  • Author(s): 末竹千博
  • Organizer: 小研究集会有限幾何学とその周辺
  • Place of Presentation: 大分大学
  • Year and Date: 2011-12-11
• [Presentation] EA(4)上の一般アダマール行列 (2010)
  • Author(s): 末竹千博
  • Organizer: Hadamard行列とそれに関係する代数的組合せ論
  • Place of Presentation: 神戸学院大学
  • Year and Date: 2010-12-12
• [Presentation] 対応するSTDが位数2のelationを持つGH(GF(4), m)とGH(GF(4), 5) (2010)
  • Author(s): 末竹千博
  • Organizer: 小研究集会有限幾何学とその周辺
  • Place of Presentation: 熊本大学
  • Year and Date: 2010-11-13
• [Presentation] 対応するSTDが位数2のelationを持つGH(GF(4),m)とGH(GH(4),5) (2010)
  • Author(s): 末竹千博
  • Organizer: 小研究集会「有限幾何とその周辺」
  • Place of Presentation: 熊本大学教育学部
  • Year and Date: 2010-11-13
• [Presentation] Generalized Hadamard matrices GH(4, 2m) over GF(4) (2010)
  • Author(s): 秋山献之, 末竹千博, 田中正紀
  • Organizer: 2010 Algebraic and geometric combinatrics conference
  • Place of Presentation: 韓国慶州Concordeホテル
  • Year and Date: 2010-07-15
• [Presentation] Generalized Hadamard matrices GH(4,2m) over GF(4) (2010)
  • Author(s): K.Akiyama, C.Suetake, M.Tanaka
  • Organizer: 2010 Algebraic and geometric combinatorics conference
  • Place of Presentation: 韓国 慶州 Concordeホテル
  • Year and Date: 2010-07-15
• [Presentation] Generalized Hadamard matrices over GF(4) and Hadamard matrices (2010)
  • Author(s): 秋山献之, 末竹千博, 田中正紀
  • Organizer: 第27回代数的組合せ論シンポジウム
  • Place of Presentation: 高知大学
  • Year and Date: 2010-06-22
• [Presentation] Generalized Hadamard matrices over GF(4)and Hadamard matices (2010)
  • Author(s): K.Akiyama, C.Suetake, M.Tanaka
  • Organizer: 第27回代数的組合せ論シンポジウム
  • Place of Presentation: 高知大学
  • Year and Date: 2010-06-22
• [Presentation] GF(4)上の一般アダマール行列の構成とそれに付随したアダマール行列 (2010)
  • Author(s): 末竹千博
  • Organizer: 小研究集会有限幾何学とその周辺
  • Place of Presentation: 熊本大学
  • Year and Date: 2010-05-08
• [Presentation] GF(4)上の一般アダマール行列の構成とそれに付随したアダマール行列 (2010)
  • Author(s): 末竹千博
  • Organizer: 小研究集会「有限幾何とその周辺」
  • Place of Presentation: 熊本大学教育学部
  • Year and Date: 2010-05-08
• [Presentation] 対称横断デザインSTD_8[24 ; 3]について (2010)
  • Author(s): 鳩野哲平, 末竹千博
  • Organizer: 第122回日本数学会九州支部例会
  • Place of Presentation: 九州大学西新プラザ
  • Year and Date: 2010-02-13
• [Presentation] 対称横断デザインSTD_8[24;3]について (2010)
  • Author(s): 末竹千博, 鳩野哲平
  • Organizer: 第122回日本数学会九州支部例会
  • Place of Presentation: 九州大学西新プラザ
  • Year and Date: 2010-02-13
• [Presentation] クラス正則対称横断デザインSTD_5[20 ; 4]についてと直交配列OA(80, 12, 4, 2)の存在 (2009)
  • Author(s): 秋山献之, 末竹千博, 田中正紀
  • Place of Presentation: 信州大学
  • Year and Date: 2009-11-19
• [Presentation] クラス正則対称横断デザインSTD_5[20;4] についてと直交配列OA(80,12,4,2)の存在 (2009)
  • Author(s): 秋山献之, 末竹千博, 田中正紀
  • Organizer: 代数的組合せ論および関連する群と代数
  • Place of Presentation: 信州大学
  • Year and Date: 2009-11-19
• [Presentation] STD_λ[3λ; 3]'s(λ<=7)の分類について (2009)
  • Author(s): 秋山献之, 末竹千博
  • Organizer: 小研究集会有限幾何学とその周辺
  • Place of Presentation: 近畿大学
  • Year and Date: 2009-10-17
• [Presentation] STD_λ[3λ;3]'sλ<=7)の分類について (2009)
  • Author(s): 秋山献之, 末竹千博
  • Organizer: 小研究集会 有限幾何とその周辺
  • Place of Presentation: 近畿大学
  • Year and Date: 2009-10-17
• [Presentation] STD_6[18, 3]' and STD_7[21, 3]'s admitting a semiregular automorphism group of order 9 (2009)
  • Author(s): 秋山献之, 小川雅之, 末竹千博
  • Organizer: 第26回代数的組合せ論シンポジウム
  • Place of Presentation: 山形県生涯学習センター
  • Year and Date: 2009-06-24
• [Presentation] On STD_6[18;3]'s and STD_7[21;3]'s admitting a semiregular automorphism group of order 9 (2009)
  • Author(s): 秋山献之, 小川雅之, 末竹千博
  • Organizer: 第26回代数的組合せ論シンポジウム
  • Place of Presentation: 山形県生涯学習センター
  • Year and Date: 2009-06-24
• [Presentation] クラスサイズ4の対称横断デザインについて (2009)
  • Author(s): 末竹千博
  • Organizer: ミニ研究集会有限幾何学とその周辺
  • Place of Presentation: 東海大学阿蘇キャンパス
  • Year and Date: 2009-05-16
• [Presentation] クラスサイズ4の対称横断デザインについて (2009)
  • Author(s): 末竹千博
  • Organizer: ミニ研究集会 有限幾何学とその周辺
  • Place of Presentation: 東海大学阿蘇キャンパス
  • Year and Date: 2009-05-16