Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part
Combinatorics
2019-01-11 v2
Abstract
The symmetric edge polytopes of odd cycles (del Pezzo polytopes) are known as smooth Fano polytopes. In this paper, we show that if the length of the cycle is 127, then the Ehrhart polynomial has a root whose real part is greater than the dimension. As a result, we have a smooth Fano polytope that is a counterexample to the two conjectures on the roots of Ehrhart polynomials.
Keywords
Cite
@article{arxiv.1109.0791,
title = {Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part},
author = {Hidefumi Ohsugi and Kazuki Shibata},
journal= {arXiv preprint arXiv:1109.0791},
year = {2019}
}
Comments
4 pages, We changed the order of the auhors and omitted a lot of parts of the paper. (If you are interested in omitted parts, then please read v1)