Matchings in permutations
Combinatorics
2026-05-07 v1 Discrete Mathematics
Abstract
We say that two permutations intersect if they map some element to the same element . A matching in a family of permutations is a collection of pairwise disjoint permutations. In this paper, we study families of permutations with no matchings of size . In particular, we obtain a characterization of the largest -matching-free families and a Hilton--Milner type result. We also obtain results for the families of derangements.
Cite
@article{arxiv.2605.04987,
title = {Matchings in permutations},
author = {Eduard Inozemtsev and Dmitrii Kolupaev and Andrey Kupavskii},
journal= {arXiv preprint arXiv:2605.04987},
year = {2026}
}