| Project/Area Number |
24540144
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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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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokai University |
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Principal Investigator |
Sakai Toshinori 東海大学, 高輪教養教育センター, 教授 (20267842)
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| Research Collaborator |
URRUTIA Jorge メキシコ国立自治大学, 数学研究所, 専任上級研究員レベルC
HURTADO Ferran カタルーニャ工科大学(スペイン), 応用数学科II, 教授
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 重み付き点集合 / 単調多角形 / 単調無交差道 / 島 / 国際研究者交流（メキシコ） / 国際情報交換（スペイン） / 国際研究者交流 / メキシコ：スペイン |
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| Outline of Final Research Achievements |
Let P be a set of n points in general position in the plane, with weights 1, 2, ..., n. A monotonic path is a path connecting points of P along which the weights of its vertices monotonically increase or decrease. A monotonic polygon is a simple polygon whose perimeter consists of a non-crossing monotonic path and an edge. A subset S of P is called an island if S consists of the points of P contained in the convex hull of S. We studied the problems concerning the maximum number of vertices contained in monotonic polygons or non-crossing monotonic paths; the maximum number of the sums of weights of vertices of monotonic polygons; the number of faces contained in a decomposition of the convex hull of P into monotonic polygons; the existence of an island with weight close to a given number; the existence of disjoint islands each of which has weight close to a given number; and so on. We also obtained some results concerning the islands of weighted point sets in d-dimensional space.
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