An analogue of the Erd{\H o}s Matching Conjecture for permutations with fixed number of cycles

Cheng Yeaw Ku, Kok Bin Wong

Let $S_n$ denote the set of permutations of $[n]=\{1,2,\dots ,n\}$. For each integer $k\ge 1$, let $S_{n,k}$ be the set of all permutations of $[n]$ with exactly $k$ disjoint cy…