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

翻译：我们称两个排列$[n]\to [n]$相交，如果它们将某个元素$x$映射到同一个元素$y$。一个排列族中的匹配是指一组两两不相交的排列。在本文中，我们研究不含大小为$s$的匹配的排列族。特别地，我们得到了最大无$s$匹配族的刻画以及一个Hilton–Milner型结果。我们还得到了错排族的相关结果。