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Combinatorial properties on convex sets by a finite point set

Research Project

Project/Area Number 21540145
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 InstitutionTokai University

Principal Investigator

URABE Masatsugu  東海大学, 清水教養教育センター, 教授 (30256177)

Co-Investigator(Kenkyū-buntansha) FUJII Nobuhiko  東海大学, 清水教養教育センター, 教授 (60228955)
AKIYAMA Masatoshi  東海大学, 清水教養教育センター, 教授 (50246146)
HOSONO Kiyoshi  東海大学, 清水教養教育センター, 教授 (40238754)
Co-Investigator(Renkei-kenkyūsha) HOSONO Kiyishi  東海大学, 清水教養育センター, 教授 (40238754)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywords応用数学 / 組合せ論 / 離散幾何学 / 離散数学
Research Abstract

"Find the smallest integer f(k) so that any set of f(k) points in the plane, no three collinear, contains the vertices of a convex k-gon, whose interior contains no points of the set. "The above problem for k=6 is a famous open problem. Our main purpose is to settle the question of the existence of f(6). Furthermore, we tried to find and solve other several discrete geometry problems for a finite point set in this research project.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (20 results)

All 2011 2010 2009

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (17 results)

  • [Journal Article] On an empty triangle with the maximum area in planar point sets2011

    • Author(s)
      Kiyoshi Hosono
    • Journal Title

      Discrete Mathematics

      Volume: Vol.311 Pages: 1886-1891

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The John-Nirenberg Inequality for Ergodic Systems2009

    • Author(s)
      Lasha Ephremidze and Nobuhiko Fujii
    • Journal Title

      Far East Journal of Dynamical Systems

      Volume: Vol.11 Pages: 49-56

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The John-Nirenberg inequality for ergodic systems2009

    • Author(s)
      Lasha Ephremidze, Nobuhiko Fujii
    • Journal Title

      Far East Journal of Dynamical Systems 11

      Pages: 49-56

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] On disjoint empty convex polygons for a planar point set2011

    • Author(s)
      Kiyoshi Hosono、Masatsugu Urabe
    • Organizer
      Japan Conference on Discrete and Computational Geometry
    • Place of Presentation
      Tokai University, Tokyo
    • Year and Date
      2011-11-28
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] A method to obtain L^p-boundedness from weak type conditions2011

    • Author(s)
      Nobuhiko Fujii
    • Organizer
      Continuum Mechanics and Related Problems of Analysis
    • Place of Presentation
      Tbilisi State University, Georgia
    • Year and Date
      2011-09-12
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Empty disks supported by a point set2011

    • Author(s)
      Kiyoshi Hosono、Masatsugu Urabe
    • Organizer
      XIV Spanish Meeting on Computational Geometry
    • Place of Presentation
      Universidad de Alcala, Spain
    • Year and Date
      2011-06-28
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] 東太平洋赤道域における海水中CO_2分圧の変動に関する研究2010

    • Author(s)
      秋山正寿、山崎淳市
    • Organizer
      海洋理工学会平成22年度秋季大会
    • Place of Presentation
      京都大学
    • Year and Date
      2010-10-13
    • Related Report
      2011 Final Research Report
  • [Presentation] 東太平洋赤道域における海水中CO_2分圧の変動に関する研究2010

    • Author(s)
      秋山正寿、山崎淳市
    • Organizer
      海洋理工学会平成22年度秋季大会
    • Place of Presentation
      京都大学吉田キャンパス
    • Year and Date
      2010-10-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] On an empty triangle with the maximum area in planar point sets2009

    • Author(s)
      Kiyoshi Hosono
    • Organizer
      The 7th Japan Conference on Computational Geometry and Graphs, 2009
    • Place of Presentation
      Japan Advanced Institute of Science and Technology
    • Year and Date
      2009-11-11
    • Related Report
      2011 Final Research Report
  • [Presentation] Gridded Data Set of Global Surface Fluxes constructed by Satellite Data : J-OFURO V22009

    • Author(s)
      Kunio Kutsuwada、Masatosi Akiyama
    • Organizer
      International Symposium on Remote Sensing 2009
    • Place of Presentation
      Pukyong National University
    • Year and Date
      2009-10-29
    • Related Report
      2011 Final Research Report
  • [Presentation] Gridded Data Set of Global Surface Fluxes constructed by Satellite Data:J-OFURO V22009

    • Author(s)
      Kunio Kutsuwada, Masatosi Akiyama
    • Organizer
      International Symposium on Remote Sensing 2009
    • Place of Presentation
      Pukyong National University
    • Year and Date
      2009-10-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] Variable exponent spacesと特異積分2009

    • Author(s)
      藤井信彦
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-24
    • Related Report
      2011 Final Research Report
  • [Presentation] Variable exponent spacesと特異積分2009

    • Author(s)
      藤井信彦
    • Organizer
      日本数学会秋季総合分科会実函数論
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] INTRODUCTION OF JAPANESE OCEAN FLUX DATA WITH USE OF REMOTE SENSING OBSERVATIONS(J-OFURO) VERSION 22009

    • Author(s)
      Masahisa Kubota、Masatosi Akiyama
    • Organizer
      Ocean Obs' 09
    • Place of Presentation
      Venice Convention Centre, Venice-Lido, Italy
    • Year and Date
      2009-09-09
    • Related Report
      2011 Final Research Report
  • [Presentation] INTRODUCTION OF JAPANESE OCEAN FLUX DATA WITH USE OF REMOTE SENSING OBSERVATIONS(J-OFURO)VERSION 22009

    • Author(s)
      Masahisa Kubota, Masatosi Akiyama
    • Organizer
      OceanObs'09
    • Place of Presentation
      Venice Convention Centre, Venice-Lido, Italy
    • Year and Date
      2009-09-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] On a minimal planar point set with two interior-disjoint empty convex polygons2009

    • Author(s)
      占部正承
    • Organizer
      離散数学とその応用研究集会2009
    • Place of Presentation
      茨城大学
    • Year and Date
      2009-08-10
    • Related Report
      2011 Final Research Report
  • [Presentation] On a minimal planar point set with two interior-disjoint empty convex polygons2009

    • Author(s)
      占部正承
    • Organizer
      離散数学とその応用研究集会2009
    • Place of Presentation
      茨城大学日立キャンパス
    • Year and Date
      2009-08-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] On a triangle with the maximum area in planar point sets2009

    • Author(s)
      Kiyoshi Hosono
    • Organizer
      Seminar on Discrete and Computational Geometry
    • Place of Presentation
      東海大学
    • Year and Date
      2009-07-12
    • Related Report
      2011 Final Research Report
  • [Presentation] Partitioning planar point sets into distinct holes2009

    • Author(s)
      占部正承
    • Organizer
      離散幾何とグラフ理論1日研究集会
    • Place of Presentation
      東海大学
    • Year and Date
      2009-05-23
    • Related Report
      2011 Final Research Report
  • [Presentation] Partitioning planar point sets into distinct holes2009

    • Author(s)
      占部正承
    • Organizer
      離散幾何とグラフ理論1日研究集会
    • Place of Presentation
      東海大学代々木校舎
    • Year and Date
      2009-05-23
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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