Extremal Families for Matchings in Permutations

Two permutations $σ,τ\in S_n$ are called disjoint if the composition $στ^{-1}$ has no fixed point. If a family $\mathcal F\subseteq S_n$ contains no $s$ pairwise disjoint permutations, then a simple averaging argument gives $|\mathcal F|\leq(s-1)(n-1)!$. Inozemtsev, Kolupaev and Kupavskii characteri