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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| Project Status |
Completed (Fiscal Year 2017)
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| 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)
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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 / ラムゼー理論 / ランダムウォーク / 格子点 |
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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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Report
(6 results)
Research Products
(38 results)
