The maximum measure of non-trivial 3-wise intersecting families

• 成果类型: Article
• 署名作者: Tokushige, Norihide
• 署名单位: University of the Ryukyus
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-01969-x
• 发表日期: 2024
• 页码: 643-676
• 关键词: theorem; systems; SPACES

摘要

Let g be a family of subsets of an n-element set. The family g is called non-trivial 3-wise intersecting if the intersection of any three subsets in g is non-empty, but the intersection of all subsets is empty. For a real number p ? (0, 1) we define the measure of the family by the sum of p(|G|)(1 - p)(n-|G|) over all G ? g. We determine the maximum measure of non-trivial 3-wise intersecting families. We also discuss the uniqueness and stability of the corresponding optimal structure. These results are obtained by solving linear programming problems.