Project/Area Number  09640292 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  TOKAI UNIVERSITY 
Principal Investigator 
URABE Masatsugu School of Marine Science and Technology, Department of Liberal Arts Associate Professor, 海洋学部, 助教授 (30256177)

CoInvestigator(Kenkyūbuntansha) 
KOMORI Yasuo Tokai University, School of HighTechnology for Human Welfare, Department of Lib, 開発工学部, 講師 (70234903)
HOSONO Kiyoshi Tokai University, Faculty of Science, Department of Mathematics, Assistant Profe, 理学部, 講師 (40238754)
NAKAMURA Akihiro Tokai University, School of HighTechnology for Human Welfare, Department of Lib, 開発工学部, 助教授 (80189026)
WATANABE Shin Tokai University, School of Marine Science and Technology, Department of Liberal, 海洋学部, 助教授 (70240489)
FUJII Nobuhiko Tokai University, Faculty of Science, Department of Mathematics, Professor, 理学部, 教授 (60228955)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1997 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  Discrete Geometry / Point set / Convex polygon / 組合せ論 / 離散幾何 / 凸多角形分割 / 応用数学 
Research Abstract 
We have studied some combinatorial properties for a given point set in the research project ; grantinaid for scientific research (C). In particular, we studied the problem on partitioning point set into disjoint convex polygons. Our paper "On a partition into convex polygons" which accepted the international journal : Discrete Applied Mathematics in 1996, introduced three partitioning properties ; Disjoint partition, Empty partition and General partition. Moreover we proved the result on the disjoint partition problem in space, it was also accepted the international journal : Computational Geometry : Theory and Applications. We gave the lecture concerning these partition problems on Ninth Canadian Conference on Computational Geometry at Queen's University in August 1997. Some researchers are interested in these problems and we talked about some related problems. In 1998, we have succeeded to improve the bound for disjoint partition problem with Professor K.Hosono who is one of the in
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vestigators in this research project, so we submitted such paper to the international journal in January 1998. In this paper, we introduced new method. Using this method, we were able to estimate the maximum number of disjoint convex quadrilaterals for a given point set. It is new and interesting. Professor G.Karolyi who is a Hungarian mathematician, studied the related problem that is the general partition into convex quadrilaterals, but nobody studies this problem. We submitted the paper concerning this problem to the international journal in July 1998 and gave the lecture on Tenth Canadian Conference on Computational Geometry at McGill University in August 199g. On the other hand, we also studied the related problem that is the existence of a convex polygon containing a specified number of points with Professor K.Hosono and Professor D.Avis at McGill University. We gave the lecture on Third Joint Meeting of the American Mathematical Society and the Sociedad Matematica Mexicana in December 1997 and submitted the paper to the special issue of Discrete Mathematics in honor of Helge Tverberg. Moreover, we gave the lecture concerning the special case of this problem on Japan Conference on Discrete and Computational Geometry '98 in December 1998 and we are preparing the new paper about it now. Less
