Ehrhart quasi-polynomials of rational polytopes by real dilations
Combinatorics
2026-05-12 v1
Abstract
This paper is to study the Ehrhart function of a rational -polytope , defined as the number of lattice points of dilated polytopes with real numbers . It turns out that is a quasi-polynomial of real variable in the sense that where are periodic piecewise polynomials of degree if contains the origin, and are periodic functions vanishing almost everywhere otherwise. When is a rational simplex , the coefficient functions are given explicitly in terms of vertex information of the simplex . Moreover, the reciprocity law still holds.
Cite
@article{arxiv.2605.10514,
title = {Ehrhart quasi-polynomials of rational polytopes by real dilations},
author = {Ying Cao and Beifang Chen},
journal= {arXiv preprint arXiv:2605.10514},
year = {2026}
}