2017 Fiscal Year Final Research Report
Extremal combinatorics: algebraic and probabilistic methods
| Project/Area Number |
25287031
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | University of the Ryukyus |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
前原 濶 琉球大学, 教育学部, 名誉教授 (60044921)
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| Research Collaborator |
Frankl P.
Lee S. J.
Kato M.
Katona G. O. H.
Shinohara M.
Siggers M.
Suda S.
Tanaka H.
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| 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 |
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| 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.
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| Free Research Field |
組合せ論
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