Intersecting families of permutations with a fixed number of cycles

Venkata Raghu Tej Pantangi

Let $\mathrm{Sym}(\mathrm{n},\mathrm{k})$ denote the set of permutations on $\{1,2,\dots ,n\}$ with exactly $k$ cycles. A family $\mathcal{F}\subset \mathrm{Sym}(n,k)$ is said to be intersecting if $…