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arXiv · 1803.02377

The equivariant volumes of the permutahedron

Federico Ardila·Anna Schindler·Andrés R. Vindas-Meléndez
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Abstract

We consider the action of the symmetric group $S_n$ on the permutahedron $Π_n$. We prove that if $σ$ is a permutation of $S_n$ which has $m$ cycles of lengths $l_1, \ldots, l_m$, then the subpolytope of $Π_n$ fixed by $σ$ has normalized volume $n^{m-2} \gcd(l_1, \ldots, l_m)$.

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Federico Ardila, Anna Schindler, Andrés R. Vindas-Meléndez. 2019-10-04. The equivariant volumes of the permutahedron. https://doi.org/10.1007/s00454-019-00146-2

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