Extremal combinatorics in discrete structues
| Project/Area Number |
18K03399
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12030:Basic mathematics-related
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| Research Institution | University of the Ryukyus |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 組合せ論 / 離散極値構造 / 交差族 / ハイパーグラフ / スペクトラルグラフ理論 / 極値離散構造 / ランダムグラフ / 線形計画問題 / スライスランク法 |
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| Outline of Final Research Achievements |
In this research project, we studied the extremal structures appeared in extremal combinatorics, and also discussed methods for this purpose. The two main results are as follows. We obtained an upper bound for the size of a set without a given "shape" in a vector space over a finite fields. We determined the extremal structure of the largest multiply intersecting families by using the corresponding spectral information.
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| Academic Significance and Societal Importance of the Research Achievements |
上に述べた成果のうち、(1)については「非退化な」解を含まない集合に関する研究において、より強い「非退化性」を定式化し解析したことに意義がある。この視点はこの分野に新しい方向を与え、その後、SauermannやEllenbergによってさらに発展している。交差族を調べる手法はいろいろあるが、現在のところ(2)の成果は固有値を用いる手法によってのみ得られており、この点に特徴がある。
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Report
(6 results)
Research Products
(17 results)
