Work

Harmonics and graded Ehrhart theory

Year: 2026

Type: article

Abstract: The Ehrhart polynomial and Ehrhart series count lattice points in integer dilations of a lattice polytope. We introduce and study a q -deformation of the Ehrhart series, based on the notions of harmonic spaces and Macaulay’s inverse systems for coordinate rings of finite point configurations. We conjecture that this q -Ehrhart series is a rational function, and introduce and study a bigraded algebra whose Hilbert series matches the q -Ehrhart series. Defining this algebra requires a new result on Macaulay inverse systems for Minkowski sums of point configurations.

Source: Journal of Combinatorial Algebra

DOI: 10.4171/jca/128

Authors: Victor Reiner, Brendon Rhoades

Institutions: University of Minnesota, University of California San Diego

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: RTG: Combinatorics and Algebra, Combinatorial Representation Theory