2015 Fiscal Year Final Research Report
Combinatorial properties of weighted point sets in the plane
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 |
Section | 一般 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Tokai University |
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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Keywords | 重み付き点集合 / 単調多角形 / 単調無交差道 / 島 |
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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Free Research Field |
離散幾何学
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