References & Citations
Mathematics > Combinatorics
Title: Non-trivial $r$-wise agreeing families
(Submitted on 22 Apr 2024 (v1), last revised 4 May 2024 (this version, v2))
Abstract: A family of sets 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.
Submission history
From: Andrey Kupavskii [view email][v1] Mon, 22 Apr 2024 13:49:43 GMT (6kb)
[v2] Sat, 4 May 2024 10:19:19 GMT (6kb)
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