Extremal Families for Matchings in Permutations

Mengyu Cao, Haixiang Zhang

Two permutations $\sigma ,\tau \in S_n$ are called disjoint if the composition $\sigma {\tau }^{-1}$ has no fixed point. If a family $\mathcal{F}\subseteq S_n$ contains no $s$ pairwise disjoint permutati…