The equivariant Ehrhart theory of the permutahedron
Federico Ardila, Mariel Supina, Andr\'es R. Vindas-Mel\'endez
TL;DR
This paper explores the equivariant Ehrhart theory of the permutahedron, providing a detailed description and confirming a conjecture related to lattice point enumeration under group actions.
Contribution
It offers the first complete description of the equivariant Ehrhart theory for the permutahedron and proves Stapledon's Effectiveness Conjecture in this context.
Findings
Confirmed Stapledon's Effectiveness Conjecture for the permutahedron
Provided explicit equivariant Ehrhart polynomial descriptions
Enhanced understanding of lattice point enumeration with symmetry
Abstract
Equivariant Ehrhart theory enumerates the lattice points in a polytope with respect to a group action. Answering a question of Stapledon, we describe the equivariant Ehrhart theory of the permutahedron, and we prove his Effectiveness Conjecture in this special case.
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