On Some Numbers Related to the Erdös-Szekeres Theorem

• 作者: Mark J. Nielsen William Webb
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Erdos-Szekeres THEOREM Combinatorial GEOMETRY
• 年，卷（期）: 2013,（3）
• 页码范围: 167-173
• 页数: 7页
• 分类号: O1

摘要

A crossing family of segments is a collection of segments each pair of which crosses. Given positive integers j and k,a(j,k) grid is the union of two pairwise-disjoint collections of segments (with j and k members, respectively) such that each segment in the first collection crosses all members of the other. Let c(k) be the least integer such that any planar set of c(k) points in general position generates a crossing family of k segments. Also let #(j,k) be the least integer such that any planar set of #(j,k) points in general position generates a (j,k)-grid. We establish here the facts 9≤c(3)≤16 and #(1,2)=8.