Ehrhart Spectra of Large Subsets in Zr

Artikel i vetenskaplig tidskrift, 2026

This paper introduces and studies the Ehrhart spectrum of a set E subset of Zr, defined as the set of all Ehrhart polynomials of simplices with vertices in E, generalizing the notion of volume spectrum. We show that for any E subset of Zr with positive upper Banach density, there is some n is an element of Z such that the Ehrhart spectrum of nZr is contained in the Ehrhart spectrum of E, generalizing an earlier result by the first and third authors for the volume spectrum of E.