The equivariant volumes of the permutahedron

Federico Ardila, Anna Schindler, Andrés R. Vindas-Meléndez

We consider the action of the symmetric group $S_n$ on the permutahedron ${\Pi }_n$. We prove that if $\sigma$ is a permutation of $S_n$ which has $m$ cycles of lengths $l_1,\dots ,l_m$, t…