English

Matchings in permutations

Combinatorics 2026-05-07 v1 Discrete Mathematics

Abstract

We say that two permutations [n][n][n]\to [n] intersect if they map some element xx to the same element yy. 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 ss. In particular, we obtain a characterization of the largest ss-matching-free families and a Hilton--Milner type result. We also obtain results for the families of derangements.

Keywords

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}
}
R2 v1 2026-07-01T12:52:55.796Z