Metrics on permutations with the same peak set

Alexander Diaz-Lopez, Kathryn Haymaker, Kathryn Keough +2

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