Harmonics and graded Ehrhart theory
Combinatorics
2024-09-25 v3 Commutative Algebra
Abstract
The Ehrhart polynomial and Ehrhart series count lattice points in integer dilations of a lattice polytope. We introduce and study a -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 -Ehrhart series is a rational function, and introduce and study a bigraded algebra whose Hilbert series matches the -Ehrhart series. Defining this algebra requires a new result on Macaulay inverse systems for Minkowski sums of point configurations.
Cite
@article{arxiv.2407.06511,
title = {Harmonics and graded Ehrhart theory},
author = {Victor Reiner and Brendon Rhoades},
journal= {arXiv preprint arXiv:2407.06511},
year = {2024}
}
Comments
61 pages. Version 3: This version features a streamlined proof of Theorem 1.4, based on a suggestion of Ian Cavey