Smooth polytopes with negative Ehrhart coefficients
arXiv:1704.05532
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.
15 pages, 1 figure, 1 table, accepted by Journal of Combinatorial Theory Ser. A