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

我们已经研究了研究项目中给定点设置的一些组合性能。科学研究授予（C）。特别是，我们研究了将分区点设置为脱节凸多边形的问题。我们的论文“关于凸多边形的分区”，该论文接受了《国际杂志：1996年的离散应用数学》，引入了三个分区属性；脱节分区，空分区和通用分区。此外，我们证明了空间中的不相交分区问题的结果，它也被接受了国际期刊：计算几何：理论和应用。我们于1997年8月在皇后大学举行的第九加拿大计算几何学会议上进行了有关这些分区问题的讲座。一些研究人员对这些问题感兴趣，我们谈到了一些相关问题。在1998年，我们成功地与K.Hosono教授的脱节分区问题改善了，后者是该研究项目中更多的遗物者之一，因此我们于1998年1月向国际期刊提交了该论文。在本文中，我们引入了新方法。使用此方法，我们能够估算给定点集的最大分离凸四次凸出数量。这是新有趣的。 G.Karolyi教授是匈牙利数学家，研究了相关的问题，该问题是凸四方的一般分区，但没有人研究这个问题。我们将有关此问题的论文提交了1998年7月的国际日报，并在8月199日在麦吉尔大学举行的第十届加拿大计算几何学会议上进行了演讲。另一方面，我们还研究了相关问题，该问题是存在凸多边形的相关问题，该问题包含了与K.Hosono教授和McGill大学教授的指定积分数量。我们于1997年12月就美国数学学会和墨西哥社会Matematica Sociedad Matematica进行了第三次联合会议的演讲，并将论文提交了离散数学特刊，以纪念Helge Tverberg。此外，我们在1998年12月在日本离散和计算几何学'98会议上发表了有关此问题的特殊情况的讲座，现在我们正在准备有关此问题的新论文。较少的