Séminaire Lotharingien de Combinatoire, 93B.48 (2025), 12 pp.
Akihiro Higashitani
Equivariant γ-Nonnegativity of Order Polytopes of Graded Posets
Abstract.
The equivariant Ehrhart theory of lattice polytopes has been introduced by Stapledon, developed by many researchers,
and the study of the equivariant h*-polynomials is getting one of the trends in the theory of lattice polytopes.
On the other hand, the h*-polynomials of order polytopes of sign-graded posets are known to be γ-nonnegative by Brändén.
In this manuscript, we prove that order polytopes of sign-graded posets are always equivariant γ-nonnegative.
Namely, the γ-polynomials of the equivariant h*-polynomials of order polytopes of graded posets have its coefficients with actual characters.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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