Ehrhart Theory over Abelian Group Rings
Robert Davis, Jes\'us A. De Loera, Alexey Garber, Katharina Jochemko, Josephine Yu
TL;DR
This paper explores Ehrhart series with coefficients in Abelian group rings, unifying various existing variants and enabling new enumeration applications in combinatorics.
Contribution
It introduces a framework for Ehrhart series over Abelian group rings, connecting polynomial weighted, q-weighted, and equivariant Ehrhart series.
Findings
Unified Ehrhart series variants within Abelian group rings
Enabled new enumeration applications in combinatorics
Connected different Ehrhart series frameworks
Abstract
We study Ehrhart series with coefficients in Abelian group rings. This opens new enumeration applications and unifies earlier variants, in particular, polynomial weighted, -weighted, and equivariant Ehrhart series.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Rings, Modules, and Algebras