Union-closed families with small average overlap densities

2020/12/06 by David Ellis, Ellis, David
Mathematics · #05D05 #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · doi:10.48550/arxiv.2012.03235

openalex publication_date 2020/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this very short paper, we point out that the average overlap density of a union-closed family F of subsets of \1,2,…,n\ may be as small as Θ((log log |F|)/(log |F|)), for infinitely many positive integers n.

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