Non-empty pairwise cross-intersecting families
Yang Huang, Yuejian Peng

TL;DR
This paper establishes a sharp upper bound for the weighted sum of sizes of non-empty pairwise cross-intersecting families of sets, generalizing previous results and allowing applications for smaller set sizes than previously possible.
Contribution
It provides a unified extremal bound for such families, characterizes the extremal families, and introduces novel techniques involving lexicographic order and unimodality analysis.
Findings
Sharp upper bound for sum of weighted family sizes
Characterization of extremal families achieving the bound
Application to cases with smaller n than k_1 + k_2
Abstract
Two families and are cross-intersecting if for any and . We call families pairwise cross-intersecting families if and are cross-intersecting when . Additionally, if for each , then we say that are non-empty pairwise cross-intersecting. Let be non-empty pairwise cross-intersecting families with , , and be positive numbers. In this paper, we give a sharp upper bound of and…
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Taxonomy
Topicsgraph theory and CDMA systems · Limits and Structures in Graph Theory · Advanced Graph Theory Research
