Combinatorial properties on convex polygons by a point set

点集凸多边形的组合属性

基本信息

批准号：
13640137
负责人：
URABE Masatsugu
金额：
$ 1.79万
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：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

项目摘要

We have studied some combinatorial properties on convex polygons by a given point set in the research project ; giant-in-aid for scientific research (C)(2). In particular, we studied the following five problems.1.Partitioning a point set into convex polygons : In our paper "On a partition into convex polygons" which has accepted to DAM in 1996, we introduced some partitioning properties ; disjoint partition, empty partition and general partition. In 2001. we have succeeded to improve the bound for disjoint partition problem with Professor K.Hosono who is one of the investigators in this research project. About empty partition, we also improved the bounds after we attended the International Congress of Mathematicians 2002 in China. We gave the talk concerning this topic on the other international conference in 2002, and this paper was accepted.2.On the existence of a convex polygon with a specified number of interior points : The paper about this topics was accepted to DM in 2001, and w … More e studied more the existence of such convex polygon with K.Hosono and G.Karolyi who is a Hungarian mathematician. In 2001, we talked around it, and this manuscript was accepted to Discrete Geometry (A.Bezdek ed.) in 2003.3.On the number of disjoint convex k-gons for a planar point set : We estimated the number of convex k-gons for a planar point set. For a convex quadrilateral, in particular, we studied, and the paper accepted in 2001. In this paper, we introduced useful partitioning method for a given point set, and then the number of convex quadrilaterals is increase in the above problem 1.4.On convex decompositions of points : We seek a partition of a given point into convex cells such that the union of the cells forms a simple polygon and every point is on the boundary. The paper concerning this topics was accepted the international journal in 2001.5.On a triangle with the maximum area in a planar point set : After I attended the international conference in 2002, I studied this problem with some colleagues in our private seminar. It is the problem about the ratio between the maximum area of an empty triangle with vertices in a planar point set and the area of the convex hull of the points. We gave the talk about this problem in the Indonesia -Japan joint conference in 2003, and submitted this manuscript. Less

我们已经通过研究项目中的给定点研究了凸多边形上的一些组合性能。科学研究的巨型（C）（2）。特别是，我们研究了以下五个问题。1。将一个点设置为凸多边形：在我们的论文中，“关于凸多边形的分区”，该分区于1996年被大坝接受，我们引入了一些分区属性；脱节分区，空分区和通用分区。在2001年，与该研究项目的研究人员之一K.Hosono教授的脱节分区问题成功改善了界限。关于空分区，我们在2002年国际数学家大会参加了中国的国际大会之后，我们还提高了界限。我们在2002年的另一个国际会议上发表了有关该主题的演讲，并接受了本文。2。在具有指定数量的内部点的凸多边形的存在：关于此主题的论文在2001年接受了DM的接受，并且更多地研究了与K.Hosono和G.Karoly and G.Karoly andation an Hungari的convex Polygon的存在。在2001年，我们围绕它进行了讨论，该手稿被接受于2003.33.的离散几何形状（A.Bezdek Ed。）。 For a convex quadrilateral, in particular, we studied, and the paper accepted in 2001. In this paper, we introduced useful partitioning method for a given point set, and then the number of convex quadrilaterals is increased in the above problem 1.4.On convex decompositions of points : We seek a partition of a given point into convex cells such that the union of the cells forms a simple polygon and every point is on the boundary.关于该主题的论文在2001年被接受了国际日报。这是关于平面点集中的顶点的最大三角形的最大面积与点凸的面积之间的问题。我们在2003年的印度尼西亚 - 日本联合会议上发表了关于这个问题的讨论，并提交了此手稿。较少的