Combinatorial properties on convex sets by a finite point set
| Project/Area Number |
21540145
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokai University |
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Principal Investigator |
URABE Masatsugu 東海大学, 清水教養教育センター, 教授 (30256177)
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| 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)
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| Co-Investigator(Renkei-kenkyūsha) |
HOSONO Kiyishi 東海大学, 清水教養育センター, 教授 (40238754)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| 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)
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| Keywords | 応用数学 / 組合せ論 / 離散幾何学 / 離散数学 |
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| 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.
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Report
(4 results)
Research Products
(20 results)
