Roots of Ehrhart polynomials and symmetric $δ$-vectors

Abstract

The conjecture on roots of Ehrhart polynomials, stated by Matsui et al. [15, Conjecture 4.10], says that all roots α of the Ehrhart polynomial of a Gorenstein Fano polytope of dimensionIn this paper, we observe the behaviors of roots of SSNN polynomials which are a wider class of the polynomials containing all the Ehrhart polynomials of Gorenstein Fano polytopes. As a result, we verify that this conjecture is true when the roots are real numbers or when d ≤ 5.