Séminaire Lotharingien de Combinatoire, 82B.16 (2019), 12 pp.

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

The equivariant volumes of the permutahedron

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 l₁, ..., l_m, then the subset of Π_n fixed by σ is a polytope with normalized volume n^m-2 gcd(l₁, ..., l_m).

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

The following versions are available:

PDF (105 K)
TeX version