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Probabilistic and pseudo-probabilistic methods in combinatorics and their applications

Research Project

Project/Area Number 19540119
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionThe University of Electro-Communications

Principal Investigator

ISHIGAMI Yoshiyasu  The University of Electro-Communications, 大学院・情報理工学研究科, 准教授 (50262374)

Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords組合せ論 / ラムゼー理論 / 超グラフ / 擬ランダム
Research Abstract

A theorem in graph theory called Szemeredi's regularity lemma is known to be useful in many combinatorial problems including additive number theory and others. This theorem has been expanded in a simple form. In previously known versions of this theorem, the constructions of the desired decompositions was obtained by repeating a complicated process. In this version, the desired decomposition is obtained almost surely by a one-time simple random sampling. By utilizing this advantage, this theorem is applied to several problems and its power is demonstrated.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (14 results)

All 2008 2007 Other

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (10 results) Remarks (2 results)

  • [Journal Article] Linear Ramsey numbers for bounded-degree hypergraphs2007

    • Author(s)
      Yoshiyasu ISHIGAMI
    • Journal Title

      Electronic Notes in Discrete Mathematics 29

      Pages: 47-51

    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Linear Ramsey numbers for bounded-degree hypergraphs2007

    • Author(s)
      Yoshiyasu Ishigami
    • Journal Title

      Electronic Notes in Discrete Mathematics

      Volume: 29 Pages: 47-51

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] A simple construction for Szemeredi's regularity lemma2008

    • Author(s)
      石上嘉康
    • Organizer
      純粋数学及び応用数学としての組合せ論・離散数学そしてその周辺ワークショップ
    • Place of Presentation
      電気通信大学
    • Year and Date
      2008-07-05
    • Related Report
      2010 Final Research Report
  • [Presentation] A simple construction for Szemeredi' s regularity lemma2008

    • Author(s)
      石上嘉康
    • Organizer
      純粋数学及び応用数学としての組合せ論・離散数学そしてその周辺ワークショップ
    • Place of Presentation
      電気通信大学
    • Year and Date
      2008-07-05
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] A simple construction for Szemeredi's regularity lemma2008

    • Author(s)
      石上嘉康
    • Organizer
      離散数学及び応用数学としての組合せ論・離散数学そしてその周辺ワークショップ
    • Place of Presentation
      電気通信大学
    • Year and Date
      2008-07-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] 離散構造の中の擬ランダム性(Szemerediの一様化補題、ランダムサンプリング、プロパティテスト、ラムゼー理論)2008

    • Author(s)
      石上嘉康
    • Organizer
      第4回組合せ論若手研究集会
    • Place of Presentation
      慶応大学理工学部
    • Year and Date
      2008-02-05
    • Related Report
      2007 Annual Research Report
  • [Presentation] A new look at Szemeredi's regularization2008

    • Author(s)
      石上嘉康
    • Organizer
      114^<th> Annual Meeting of AMS(American Mathematical Society)
    • Place of Presentation
      San Diego Convention Center, USA
    • Year and Date
      2008-01-09
    • Related Report
      2010 Final Research Report
  • [Presentation] A new look at Szemeredi' s regularization2008

    • Author(s)
      Yoshiyasu ISHIGAMI
    • Organizer
      114^<th> Annual Meeting of AMS (American Mathematical Society)
    • Place of Presentation
      San Diego Convention Center, USA
    • Year and Date
      2008-01-09
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Linear Ramsey numbers for bounded-degree hypergraphs2007

    • Author(s)
      石上嘉康
    • Organizer
      日本数学会・応用数学分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] Linear Ramsey numbers for bounded-degree hypergraphs2007

    • Author(s)
      石上嘉康
    • Organizer
      日本数学会秋季総合分科会(応用数学分科会)
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Linear Ramsey numbers for bounded-degree hypergraphs2007

    • Author(s)
      石上嘉康
    • Organizer
      Electronic Notes in Discrete Mathematics, Eurocomb 2007
    • Place of Presentation
      Seville university, Spain
    • Year and Date
      2007-09-13
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] Linear Ramsey numbers for bounded-degree hypergraphs2007

    • Author(s)
      Yoshiyasu Ishigami
    • Organizer
      Euro Combinatorics 2007
    • Place of Presentation
      Seville University, Spain
    • Year and Date
      2007-09-13
    • Related Report
      2007 Annual Research Report
  • [Remarks] Yoshiyasu Ishigami. A simple regularization of graphs. math.CO arXiv : 0904.4927

    • URL

      http://front.math.ucdavis.edu/0904.4927

    • Related Report
      2010 Final Research Report
  • [Remarks] Yoshiyasu Ishigami. The number of hypergraphs and colored Hypergraphs with hereditary properties. math.CO. arXiv : 0712.0425

    • URL

      http://front.math.ucdavis.edu/0712.0425

    • Related Report
      2010 Final Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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