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On Combinatorial Properties for a given point set in Euclidean space

欧几里得空间中给定点集的组合性质

基本信息

批准号：
09640292
负责人：
URABE Masatsugu
金额：
$ 1.34万
依托单位：
TOKAI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640292/
关键词：
Discrete Geometry Point set Convex polygon 応用数学

项目摘要

We have studied some combinatorial properties for a given point set in the research project ; grant-in-aid 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 … More 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

我们研究了研究项目中给定点集的一些组合性质；科学研究助学金(C)。特别地，我们研究了将点集划分为不相交的凸多边形的问题。1996年，我们在国际期刊《离散应用数学》上发表的《关于凸多边形分划》一文中，引入了三个划分性质：不相交划分、空划分和一般划分。此外，我们还证明了关于空间不相交划分问题的结果，它也被国际期刊《计算几何：理论与应用》所接受。1997年8月，我们在女王大学举行的第九届加拿大计算几何会议上作了关于这些划分问题的演讲。一些研究人员对这些问题很感兴趣，我们讨论了一些相关的问题。1998年，我们与…中的K.Hosono教授一起成功地改进了不相交划分问题的界因此，我们在1998年1月向《国际期刊》提交了这篇论文。在本文中，我们介绍了新的方法。使用这种方法，我们能够估计给定点集的不相交凸四边形的最大数目。这是新的和有趣的。匈牙利数学家G.Karolyi教授研究了与此相关的问题，即一般的凸四边形划分问题，但没有人研究这个问题。我们在1998年7月向国际期刊提交了关于这个问题的论文，并于1999年8月在McGill大学的第十届加拿大计算几何会议上发表了演讲。另一方面，我们还与McGill大学的K.Hosono教授和D.Avis教授一起研究了相关的问题，即包含指定点数的凸多边形的存在性。1997年12月，我们在美国数学学会和墨西哥数学学会第三次联席会议上发表了演讲，并向《离散数学》特刊提交了论文，以纪念赫尔格·特弗伯格。此外，我们于1998年12月在日本离散与计算几何会议上就这一问题的特例进行了演讲，目前正在准备有关这一问题的新论文。