A Product Version of the Hilton-Milner Theorem

2022/06/15 by Péter Frankl, Jian Wang, Frankl, Peter +1 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2206.07218

openalex publication_date 2022/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two families F,G of k-subsets of \1,2,…,n\ are called non-trivial cross-intersecting if F∩ G≠ ∅ for all F∈ F, G∈ G and ∩ \F\colon F∈ F\=∅=∩ \G\colon G∈ G\. In the present paper, we determine the maximum product of the sizes of two non-trivial cross-intersecting families of k-subsets of \1,2,…,n\ for n≥ 4k, k≥ 8, which is a product version of the classical Hilton-Milner Theorem.

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• Cross-intersection theorems for uniform partitions of finite sets

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