Convex Polygons and Separation of Convex

IF 0.4 4区数学 Q4 MATHEMATICS

Studia Scientiarum Mathematicarum Hungarica Pub Date : 2022-09-24 DOI:10.1556/012.2022.01530

Eduardo Rivera-Campo, J. Urrutia

引用次数: 0

Abstract

We prove that for any collection F of n ≥ 2 pairwise disjoint compact convex sets in the plane there is a pair of sets A and B in F such that any line that separates A from B separates either A or B from a subcollection of F with at least n/18 sets.

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凸多边形与凸分离

证明了对于平面上n≥2对不相交紧凸集的任何集合F，在F中存在一对集合a和B，使得任何一条将a与B分开的直线将a或B从F的子集合中分离出至少n/18个集合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Studia Scientiarum Mathematicarum Hungarica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.