English

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