Non-trivial $r$-wise agreeing families
Combinatorics
2024-12-10 v3
Abstract
A family of subsets of is -wise agreeing if for any sets from the family there is an element that is either contained in all or contained in none of the 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 -wise agreeing family. This can be seen as a generalization of the classical Brace-Daykin theorem.
Cite
@article{arxiv.2404.14178,
title = {Non-trivial $r$-wise agreeing families},
author = {Peter Frankl and Andrey Kupavskii},
journal= {arXiv preprint arXiv:2404.14178},
year = {2024}
}