The maximum sum of sizes of non-empty cross t-intersecting families

2023/12/30 by Shuang Li, Dehai Liu, Li, Shuang +5
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2401.00253

openalex publication_date 2023/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let [n]:=\lbrace 1,2,…,n \rbrace, and M be a set of positive integers. Denote the family of all subsets of [n] with sizes in M by \binom[n]M. The non-empty families A⊆\binom[n]R and B⊆ \binom[n]S are said to be cross t-intersecting if |A∩ B|≥ t for all A∈ A and B∈ B. In this paper, we determine the maximum sum of sizes of non-empty cross t-intersecting families, and characterize the extremal families. Similar result for finite vector spaces is also proved.

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