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Groebner bases of ideals and rings related with invariant polynomials and its application to information science

Research Project

Project/Area Number 18740018
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionRikkyo University

Principal Investigator

HIDEFUMI Ohsugi  Rikkyo University, 理学部, 准教授 (80350289)

Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥2,740,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords環論 / グレブナー基底 / トーリックイデアル / 不変式 / 誤り訂正符号
Research Abstract

本研究では,グレブナー基底の理論を活用して,有限群の不変式に纏わるイデアルや,対称性の高い生成系を持つイデアルなどを解析し,情報科学,統計学への応用を目的として研究を行った。その結果,ヒルベルトイデアルの(普遍)グレブナー基底や,豊富な対称性を持つ配置(セグレ・ベロネーゼ配置,ネストされた配置など)に付随するトーリックイデアルやトーリック環について環論的な性質などの解明に成功した。

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (20 results)

All 2009 2008 2007 2006 Other

All Journal Article (10 results) (of which Peer Reviewed: 9 results) Presentation (8 results) Book (2 results)

  • [Journal Article] Two way subtable sum problems and quadratic Grobner bases2009

    • Author(s)
      Hidefumi Ohsugi and Takayuki Hibi
    • Journal Title

      Proceedings of the AMS 137

      Pages: 1539-1542

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Two way subtable sum problems and quadratic Grobner bases2009

    • Author(s)
      H. Ohsugi and T. Hibi
    • Journal Title

      Proceedings of the AMS 137

      Pages: 1539-1542

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Grobner bases of nested configurations2008

    • Author(s)
      Satoshi Aoki, Takayuki Hibi, Hidefumi Ohsugi and Akimichi Takemura
    • Journal Title

      Journal of Algebra 320

      Pages: 2583-2593

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Grobner bases of nested configurations2008

    • Author(s)
      S. Aoki, T. Hibi, H. Ohsugi and A. Takemura
    • Journal Title

      Journal of Algebra 320

      Pages: 2583-2593

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A geometric definition of combinatorial pure subrings and Grobner bases of toric ideals of positive roots2007

    • Author(s)
      Hidefumi Ohsugi
    • Journal Title

      Comment. Math. Univ. St. Pauli 56no.1

      Pages: 27-44

    • NAID

      110007689220

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A geometric definition of combinatorial pure subrings and Groebner bases of toric ideals of positive roots2007

    • Author(s)
      Hidefumi Ohsugi
    • Journal Title

      Comment. Math. Univ. St. Pauli 56, no.1

      Pages: 27-44

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Grobner bases of Hilbert ideals ofalternating groups2006

    • Author(s)
      Takashi Wada and Hidefumi Ohsugi
    • Journal Title

      Journal of Symbolic Computation 41 No.8

      Pages: 905-908

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gr□bner bases of Hilbert ideals of alternating groups2006

    • Author(s)
      Takashi Wada
    • Journal Title

      Journal of Symbolic Computation 41・No.8

      Pages: 905-908

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Unmixed bipartite graphs and sublattices of the Boolean lattices

    • Author(s)
      Juergen Herzog, Takayuki Hibi and Hidefumi Ohsugi
    • Journal Title

      Journal of Algebraic Combinatorics (in press)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Markov basis and Grobner basis of Segre-Veronese configuration for testing independence in group-wise selections

    • Author(s)
      Satoshi Aoki, Takayuki Hibi, Hidefumi Ohsugi and Akimichi Takemura
    • Journal Title

      Annals of the Institute of Statistical Mathematics (in press)

    • NAID

      40017002001

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Presentation] Unmixed bipartite graphs and sublattices of the Boolean lattices2009

    • Author(s)
      Juergen Herzog,日比孝之,大杉英史
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-29
    • Related Report
      2008 Final Research Report
  • [Presentation] Grobner bases of nested configurations2008

    • Author(s)
      青木敏,日比孝之,大杉英史,竹村彰通
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Grobner bases of nested configurations2008

    • Author(s)
      青木敏、日比孝之、大杉英史、竹村彰通
    • Organizer
      2008年日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] Simple edge polytopes2008

    • Author(s)
      大杉英史,日比孝之
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-26
    • Related Report
      2008 Final Research Report
  • [Presentation] Simple Polytopes Arising from Finite Graphs2008

    • Author(s)
      Hidefumi Ohsugi
    • Organizer
      WORLDCOMP'08
    • Place of Presentation
      アメリカ・ラスベガス
    • Related Report
      2008 Final Research Report
  • [Presentation] グループごとに制約がある選択問題の条件付検定手法とSegre-Veronese型配置のグレブナー基底2007

    • Author(s)
      青木敏,日比孝之,大杉英史,竹村彰通
    • Organizer
      日本数学会年会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2007-03-29
    • Related Report
      2008 Final Research Report
  • [Presentation] Smooth edge polytopes2007

    • Author(s)
      Hidefumi Ohsugi
    • Organizer
      Projective Normality of Smooth Toric Varieties
    • Place of Presentation
      オーバーヴォルファッハ研究所(ドイツ)
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Grobner bases of toric ideals2006

    • Author(s)
      Hidefumi Ohsugi
    • Organizer
      Efficient Computation of Grobner bases and Mathematical Algorithms Based on It
    • Place of Presentation
      韓国・KIAS
    • Related Report
      2008 Final Research Report
  • [Book] グレブナー基底の現在2006

    • Author(s)
      日比孝之
    • Publisher
      数学書房
    • Related Report
      2008 Final Research Report
  • [Book] グレブナー基底の現在(いま)2006

    • Author(s)
      日比孝之編
    • Total Pages
      245
    • Publisher
      数学書房
    • Related Report
      2006 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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