Ehrhart Spectra of Large Subsets in Zr
Journal article, 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.
simplices
multiple correlations
polynomials
Author
Michael Björklund
Chalmers, Mathematical Sciences, Analysis and Probability Theory
University of Gothenburg
Rickard Cullman
University of Gothenburg
Chalmers, Mathematical Sciences, Analysis and Probability Theory
Alexander Fish
The University of Sydney
Colloquium Mathematicum
0010-1354 (ISSN) 1730-6302 (eISSN)
Vol. In PressSubject Categories (SSIF 2025)
Mathematical sciences
DOI
10.4064/cm9704-10-2025