Coefficients and roots of peak polynomials

Sara Billey, Matthew Fahrbach, Alan Talmage

Given a permutation $\pi ={\pi }_1{\pi }_2\cdots {\pi }_n\in {\mathfrak{S}}_n$, we say an index $i$ is a peak if ${\pi }_{i-1}<{\pi }_i>{\pi }_{i+1}$. Let $P(\pi )$ denote the set of peaks of $\pi$. Given any set $S…