Combinatorial properties on convex polygons by a point set

在课题研究中，我们利用给定的点集研究了凸多边形上的一些组合性质；科学研究的巨额援助(C)。具体来说，我们研究了以下五个问题。将点集划分为凸多边形：在1996年被DAM接受的论文“On a partition into convex polygon”中，我们引入了一些划分性质；不相交分区、空分区和一般分区。在2001年。我们与本项目的研究者之一K.Hosono教授成功地改进了不相交分割问题的界。关于空分区，我们在参加2002年中国国际数学家大会后也对边界进行了改进。我们在2002年的另一届国际会议上作了关于该主题的报告，论文被采纳。关于具有指定数目内点的凸多边形的存在性：2001年，他与匈牙利数学家K.Hosono和G.Karolyi进一步研究了该类凸多边形的存在性。2001年，我们围绕它进行了讨论，并于2003年3月被《离散几何》（A.Bezdek主编）接受。关于平面点集的不相交凸k-gon的数目：我们估计了平面点集的凸k-gon的数目。特别是对于凸四边形，我们进行了研究，论文于2001年被接受。本文引入了对给定点集的有用划分方法，然后在上述问题1.4中增加凸四边形的个数。关于点的凸分解：我们寻求将给定点划分为凸单元，使得单元的并集形成一个简单多边形，并且每个点都在边界上。本课题论文于2001年被国际期刊接受。关于平面点集中面积最大的三角形：2002年参加国际会议后，我和一些同事在我们的私人研讨会上研究了这个问题。它是关于平面点集中有顶点的空三角形的最大面积与点的凸包面积之比的问题。我们在2003年的印尼-日本联合会议上做了关于这个问题的演讲，并提交了这个手稿。少

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