特定内点个数集合的存在性研究

数学季刊 ›› 2012, Vol. 27 ›› Issue (4): 606-614.

特定内点个数集合的存在性研究

1. College of Science, Hebei University of Science and Technology 2. College of Mathematics, Hebei Normal University

收稿日期:2011-06-13 出版日期:2012-12-30 发布日期:2023-03-16
作者简介:WEI Xiang-lin(1974-), female, native of Zhangjiakou, Hebei, an associate professor of Hebei University of Science and Technology, engages in combinatorial geometry and discrete geometry; DING Ren(1939-), male, native of Yongkang, Zhejiang, a professor of Hebei Normal University, engages in combinatorial geometry and discrete geometry.
基金资助:
Supported by the National Natural Science Foundation of China(10901045,11171088)； Supported by the NSF of Hebei Province(A2010000828)； Supported by the SF of Hebei University of Science and Technology(QD200955)

A Note on the Existence of a Specified Number of Interior Points

1. College of Science, Hebei University of Science and Technology 2. College of Mathematics, Hebei Normal University

Received:2011-06-13 Online:2012-12-30 Published:2023-03-16
About author:WEI Xiang-lin(1974-), female, native of Zhangjiakou, Hebei, an associate professor of Hebei University of Science and Technology, engages in combinatorial geometry and discrete geometry; DING Ren(1939-), male, native of Yongkang, Zhejiang, a professor of Hebei Normal University, engages in combinatorial geometry and discrete geometry.
Supported by:
Supported by the National Natural Science Foundation of China(10901045,11171088)； Supported by the NSF of Hebei Province(A2010000828)； Supported by the SF of Hebei University of Science and Technology(QD200955)

摘要/Abstract

摘要： An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k>1, let h(k) be the smallest integer such that every set of points in the plane, no three collinear, with at least h(k) interior points, has a subset of points with exactly k or k+1 interior points of P. We prove that h(5) = 11.

关键词: interior points, empty triangle, deficient point set, (x,y)-splitters

Abstract: An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k>1, let h(k) be the smallest integer such that every set of points in the plane, no three collinear, with at least h(k) interior points, has a subset of points with exactly k or k+1 interior points of P. We prove that h(5) = 11.

Key words: interior points, empty triangle, deficient point set, (x,y)-splitters

中图分类号:

O157.3

魏祥林, 丁仁. 特定内点个数集合的存在性研究[J]. 数学季刊, 2012, 27(4): 606-614.

WEI Xiang-lin, DING Ren. A Note on the Existence of a Specified Number of Interior Points[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(4): 606-614.