Hidefumi Ohsugi, Kazuki Shibata
Published 2011-09-05, updated 2011-11-02Version 2
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.
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)
Journal: Discrete and Computational Geometry 47 (2012), 624--628
On the gamma-vector of symmetric edge polytopes
The distribution of roots of Ehrhart polynomials for the dual of root polytopes
Roots of Ehrhart polynomials and symmetric $δ$-vectors
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