Metrics on permutations with the same descent set

Alexander Diaz-Lopez, Kathryn Haymaker, Colin McGarry +1

Let $S_n$ be the symmetric group on the set $[n]:=\{1,2,\dots ,n\}$. Given a permutation $\sigma ={\sigma }_1{\sigma }_2\cdots {\sigma }_n\in S_n$, we say it has a descent at index $i$ if ${\sigma }_i>{\sigma }_{i+1}$. Let $…