A proof of the peak polynomial positivity conjecture

Alexander Diaz-Lopez, Pamela E. Harris, Erik Insko +1

We say that a permutation $\pi ={\pi }_1{\pi }_2\cdots {\pi }_n\in {\mathfrak{S}}_n$ has a peak at index $i$ if ${\pi }_{i-1}<{\pi }_i>{\pi }_{i+1}$. Let $\mathcal{P}(\pi )$ denote the set of indices where $\pi$ has…