Non-trivial $r$-wise agreeing families

Peter Frankl; Andrey Kupavskii

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arXiv · 2404.14178

Non-trivial $r$-wise agreeing families

Peter Frankl·Andrey Kupavskii

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Abstract

A family of subsets of $[n]$ is $r$-wise agreeing if for any $r$ sets from the family there is an element $x$ that is either contained in all or contained in none of the $r$ sets. The study of such families is motivated by questions in discrete optimization. In this paper, we determine the size of the largest non-trivial $r$-wise agreeing family. This can be seen as a generalization of the classical Brace-Daykin theorem.

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Peter Frankl, Andrey Kupavskii. 2024-12-09. Non-trivial $r$-wise agreeing families. https://arxiv.org/abs/2404.14178

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