Smooth polytopes with negative Ehrhart coefficients
Combinatorics
2018-06-21 v4 Algebraic Geometry
Abstract
We present examples of smooth lattice polytopes in dimensions 3 and higher where each coefficient of their Ehrhart polynomials that can potentially be negative is indeed negative. This answers a question by Bruns. We also discuss Berline-Vergne valuations as a useful tool in proving Ehrhart positivity results.
Keywords
Cite
@article{arxiv.1704.05532,
title = {Smooth polytopes with negative Ehrhart coefficients},
author = {Federico Castillo and Fu Liu and Benjamin Nill and Andreas Paffenholz},
journal= {arXiv preprint arXiv:1704.05532},
year = {2018}
}
Comments
15 pages, 1 figure, 1 table, accepted by Journal of Combinatorial Theory Ser. A