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Extremal combinatorics: algebraic and probabilistic methods

Research Project

Project/Area Number 25287031
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionUniversity of the Ryukyus

Principal Investigator

TOKUSHIGE Norihide  琉球大学, 教育学部, 教授 (00217481)

Co-Investigator(Kenkyū-buntansha) 前原 濶  琉球大学, 教育学部, 名誉教授 (60044921)
Research Collaborator Frankl P.  
Lee S. J.  
Kato M.  
Katona G. O. H.  
Shinohara M.  
Siggers M.  
Suda S.  
Tanaka H.  
Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥6,760,000 (Direct Cost: ¥5,200,000、Indirect Cost: ¥1,560,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords組合せ論 / 極値組合せ論 / ハイパーグラフ / 極値集合論 / 交差族 / 半正定値計画 / ラムゼー理論 / ランダムウォーク / 格子点
Outline of Final Research Achievements

We studied some problems in extremal set theory by using algebraic and probabilistic methods as well as combinatorial methods. Among other results we obtained the following two major results. One is the use of semidefinite programming to solve a problem of cross intersecting families, and the other is the use of the random walk method to extend the Ahlswede-Khachatrian Theorem to cross intersecting families. In both cases we obtained sharp results.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • 2013 Annual Research Report

Research Products

(38 results)

All 2017 2016 2015 2014 2013 Other

All Journal Article (14 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 14 results,  Acknowledgement Compliant: 7 results,  Open Access: 1 results) Presentation (20 results) (of which Int'l Joint Research: 4 results,  Invited: 9 results) Book (3 results) Remarks (1 results)

  • [Journal Article] A semidefinite programming approach to a cross-intersection problem with measures2017

    • Author(s)
      Sho Suda, Hajime Tanaka, Norihide Tokushige
    • Journal Title

      Mathematical Programming

      Volume: 印刷中 Issue: 1-2 Pages: 113-130

    • DOI

      10.1007/s10107-016-1106-3

    • Related Report
      2017 Annual Research Report 2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A note on Huang-Zhao theorem on intersecting families with large minimum degree2017

    • Author(s)
      Peter Frankl, Tokushige Norihide
    • Journal Title

      Discrete Mathematics

      Volume: 340 Issue: 5 Pages: 1098-1103

    • DOI

      10.1016/j.disc.2016.10.011

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Toward extending the Ahlswede-Khachatrian theorem to cross t-intersecting families2017

    • Author(s)
      S.J.Lee, M.Sigger, N.Tokushige
    • Journal Title

      Discrete Applied Mathematics

      Volume: 216 Pages: 627-645

    • DOI

      10.1016/j.dam.2016.02.015

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Multiply union families in N^n2016

    • Author(s)
      P.Frankl, M.Shinohara, N.Tokushige
    • Journal Title

      European Journal of Combinatorics

      Volume: 58 Pages: 66-74

    • DOI

      10.1016/j.ejc.2016.05.007

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Invitation to intersection problems for finite sets2016

    • Author(s)
      P.Frankl, N.Tokushige
    • Journal Title

      Journal of Combinatorial Theory, Series A

      Volume: 144 Pages: 157-211

    • DOI

      10.1016/j.jcta.2016.06.017

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Uniform eventown problems2016

    • Author(s)
      P. Frankl, N. Tokushige
    • Journal Title

      European Journal of Combinatorics

      Volume: 51 Pages: 280-286

    • DOI

      10.1016/j.ejc.2015.06.001

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Intersection problems in the q-ary cube2016

    • Author(s)
      P. Frankl, N. Tokshige
    • Journal Title

      Journal of Combinatorial Theory (A)

      Volume: 141 Pages: 90-126

    • DOI

      10.1016/j.jcta.2016.02.006

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] An Erdos-Ko-Rado theorem for cross t-intersecting families2014

    • Author(s)
      Peter Frankl, Sang June Lee, Mark Siggers, Norihide Tokushige
    • Journal Title

      Journal of Combinatorial Theory (A)

      Volume: 128 Pages: 207-249

    • DOI

      10.1016/j.jcta.2014.08.006

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Two-colorings with many monochromatic cliques in both colors2013

    • Author(s)
      Frankl, Peter; Kato, Mitsuo; Katona, Gyula O. H.; Tokushige, Norihide
    • Journal Title

      J. Combin. Theory Ser. B

      Volume: 103 Issue: 4 Pages: 415-427

    • DOI

      10.1016/j.jctb.2013.04.002

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cross t-intersecting integer sequences from weighted Erdos-Ko-Rado2013

    • Author(s)
      Tokushige, Norihide
    • Journal Title

      Combin. Probab. Comput.

      Volume: 22 Issue: 4 Pages: 622-637

    • DOI

      10.1017/s0963548313000138

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Katona theorem for vector spaces2013

    • Author(s)
      Frankl, Peter; Tokushige, Norihide
    • Journal Title

      J. Combin. Theory Ser. A

      Volume: 120 Issue: 7 Pages: 1578-1589

    • DOI

      10.1016/j.jcta.2013.05.007

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The eigenvalue method for cross t-intersecting families2013

    • Author(s)
      Tokushige, Norihide
    • Journal Title

      J. Algebraic Combin.

      Volume: 38 Issue: 3 Pages: 653-662

    • DOI

      10.1007/s10801-012-0419-4

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Euclidean embeddings of finite metric spaces2013

    • Author(s)
      Maehara, Hiroshi
    • Journal Title

      Discrete Math.

      Volume: 313 Issue: 23 Pages: 2848-2856

    • DOI

      10.1016/j.disc.2013.08.029

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Necks of regular polyhedra2013

    • Author(s)
      Maehara, Hiroshi
    • Journal Title

      J. Geom.

      Volume: 104 Issue: 2 Pages: 329-340

    • DOI

      10.1007/s00022-013-0165-3

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Presentation] The maximum product of measure of cross t-intersecting families2017

    • Author(s)
      N. Tokushige
    • Organizer
      Recent Advances in Extremal Combinatorics Workshop (TSIMF)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The maximum product of measure of cross t-intersecting families2017

    • Author(s)
      N. Tokushige
    • Organizer
      64rd KPPY combinatorics workshop (Kyungpook National University)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A semidefinite programming approach to cross-intersection problems2016

    • Author(s)
      N. Tokushige
    • Organizer
      2016 International Workshop on Graph Theory and Combinatorics
    • Place of Presentation
      Ewha Womans University (Seoul, Korea)
    • Year and Date
      2016-02-18
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Multiply union families in N^n2016

    • Author(s)
      M. Shinohara
    • Organizer
      The 14th Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      Pusan National University (Busan, Korea)
    • Year and Date
      2016-01-29
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 最小次数の大きい集合族、部分空間族2016

    • Author(s)
      徳重典英
    • Organizer
      第33回代数的組合せ論シンポジウム
    • Place of Presentation
      ピアザ淡海(滋賀県大津市)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Intersection problems in the q-ary cube2015

    • Author(s)
      N. Tokushige
    • Organizer
      離散数学とその応用研究集会 2015
    • Place of Presentation
      熊本大学
    • Year and Date
      2015-08-22
    • Related Report
      2015 Annual Research Report
  • [Presentation] A semidefinite programming approach to a cross-intersection problem with measures2015

    • Author(s)
      H. Tanaka
    • Organizer
      第32回代数的組合せ論研究集会
    • Place of Presentation
      石川県文教会館
    • Year and Date
      2015-06-22
    • Related Report
      2015 Annual Research Report
  • [Presentation] L-systemについて2015

    • Author(s)
      N. Tokushige
    • Organizer
      第1回代数的組合せ論「仙台勉強会」
    • Place of Presentation
      東北大学
    • Year and Date
      2015-05-08
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] A semidefinite programming approach to a cross-intersection problem with measures2015

    • Author(s)
      Norihide Tokushige
    • Organizer
      The 3rd Workshop on Spectral Graph Theory and Related Topics
    • Place of Presentation
      広島工業大学(広島県)
    • Year and Date
      2015-03-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] あっ、こんなところにも線形代数が!2014

    • Author(s)
      徳重典英
    • Organizer
      自然科学研究教育センター講演会(第29回)
    • Place of Presentation
      慶應義塾大学(神奈川県)
    • Year and Date
      2014-11-07
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Intersection problems in the q-ary cube2014

    • Author(s)
      Norihide Tokushige
    • Organizer
      The 5th KIAS Combinatorics Workshop
    • Place of Presentation
      KIAS, (Seoul, 韓国)
    • Year and Date
      2014-09-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 極値集合論における線形代数手法2014

    • Author(s)
      徳重典英
    • Organizer
      RIMS共同研究「デザイン、符号、グラフおよびその周辺」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2014-07-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] Intersecting hypergraphs2014

    • Author(s)
      Norihide Tokushige
    • Organizer
      Sum(m)it 240 conference
    • Place of Presentation
      Eotvos University (Budapest, Hungary)
    • Year and Date
      2014-07-07
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Some recent results about cross intersecting families2014

    • Author(s)
      Norihide Tokushige
    • Organizer
      SIAM conference on discrete mathematics 2014
    • Place of Presentation
      Hyatt Regency Minneapolis (Minneapolis, MN)
    • Year and Date
      2014-06-17
    • Related Report
      2014 Annual Research Report
  • [Presentation] Erdos--Ko--Rado type results for cross intersecting families2014

    • Author(s)
      Norihide Tokushige
    • Organizer
      Japan conference on graph theory and combinatorics
    • Place of Presentation
      日本大学(東京都)
    • Year and Date
      2014-05-17
    • Related Report
      2014 Annual Research Report
  • [Presentation] どの色の単色クリークも多い二着色

    • Author(s)
      徳重典英
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] A ratio bound for bipartite graphs

    • Author(s)
      徳重典英
    • Organizer
      代数的グラフ理論、スペクトラルグラフ理論および周辺領域
    • Place of Presentation
      東北大学(宮城県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Egawa's list of problems in 1989

    • Author(s)
      徳重典英
    • Organizer
      Graph Theory Conference in honor of Yoshimi Egawa on the occasion of his 60th birthday
    • Place of Presentation
      東京理科大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Two-colorings with many monochromatic cliques in both colors, and some related problems

    • Author(s)
      徳重典英
    • Organizer
      8th Japanese-Hungarian symposium on discrete mathematics and its applications
    • Place of Presentation
      Pannon University (Veszprem, Hungary)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Steinhausの格子点問題 --- 再遊

    • Author(s)
      前原濶
    • Organizer
      第130回 日本数学会九州支部例会
    • Place of Presentation
      琉球大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Book] プリンストン数学大全(IV.19の訳出)2015

    • Author(s)
      ティモシー・ガワーズ
    • Total Pages
      16
    • Publisher
      朝倉書店
    • Related Report
      2015 Annual Research Report
  • [Book] 33の素敵な数学小景2014

    • Author(s)
      イジィ・マトウシェク(著) 徳重典英(訳)
    • Total Pages
      230
    • Publisher
      日本評論社
    • Related Report
      2014 Annual Research Report
  • [Book] 絵ときトポロジー ―曲面のかたち―2013

    • Author(s)
      前原 濶, 桑田 孝泰
    • Total Pages
      117
    • Publisher
      共立出版
    • Related Report
      2013 Annual Research Report
  • [Remarks] List of publication

    • URL

      http://www.cc.u-ryukyu.ac.jp/~hide/publist.html

    • Related Report
      2015 Annual Research Report

URL: 

Published: 2013-05-21   Modified: 2019-07-29  

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