Equivariant Ehrhart theory, commutative algebra and invariant triangulations of polytopes
Combinatorics
2025-09-26 v3 Commutative Algebra
Representation Theory
Abstract
Ehrhart theory is the study of the enumeration of lattice points in lattice polytopes. Equivariant Ehrhart theory is a generalization of Ehrhart theory that takes into account the action of a finite group acting via affine transformations on the underlying lattice and preserving the polytope. We further develop equivariant Ehrhart theory in part by establishing connections with commutative algebra as well as the question of when there exists an invariant lattice triangulation of a lattice polytope.
Keywords
Cite
@article{arxiv.2311.17273,
title = {Equivariant Ehrhart theory, commutative algebra and invariant triangulations of polytopes},
author = {Alan Stapledon},
journal= {arXiv preprint arXiv:2311.17273},
year = {2025}
}
Comments
45 pages; typos corrected, references updated, added Example 3.20, added introductory paragraph