Roots of Ehrhart polynomials and symmetric $δ$-vectors

Details Roots of Ehrhart polynomials and symmetric $δ$-vectors Roots of Ehrhart polynomials and symmetric $δ$-vectors

2011-12-25

arxiv.org/abs/1112.5777v1

Mathematics

Combinatorics

12 pages. I welcome your comments. This article is the version without figures. If you are interested in the version with figu

Scientific paper

The conjecture on roots of Ehrhart polynomials, stated by Matsui, the author, Nagazawa, Ohsugi and Hibi, says that all the roots $\alpha$ of the Ehrhart polynomial of a Gorenstein Fano polytope satisfy $-\frac{d}{2} \leq \Re(\alpha) \leq \frac{d}{2} -1$. In this paper, we observe the behaviors of roots of SSNN polynomials. As a result, we verify that this conjecture is true when the roots are real numbers or when $d \leq 5$.

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