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arXiv · 2506.21993

$s$-almost cross-$t$-intersecting families for finite sets

Dehai Liu·Kaishun Wang·Tian Yao
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Abstract

Two families $\mathcal{F}$ and $\mathcal{G}$ of $k$-subsets of an $n$-set are called $s$-almost cross-$t$-intersecting if each member in $\mathcal{F}$ (resp. $\mathcal{G}$) is $t$-disjoint with at most $s$ members in $\mathcal{G}$ (resp. $\mathcal{F}$). In this paper, we characterize the $s$-almost cross-$t$-intersecting families with the maximum product of their sizes. Furthermore, we provide a corresponding stability result after studying the $s$-almost cross-$t$-intersecting families which are not cross-$t$-intersecting.

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Dehai Liu, Kaishun Wang, Tian Yao. 2025-06-27. $s$-almost cross-$t$-intersecting families for finite sets. https://arxiv.org/abs/2506.21993

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