Roots of Ehrhart polynomials of Gorenstein Fano polytopes

Abstract

Given arbitrary integers $k$ and $d$ with $0\le 2k\le d$, we construct a Gorenstein Fano polytope $\Pc \subset \RR^d$ of dimension $d$ such that (i) its Ehrhart polynomial $i(\Pc, n)$ possesses $d$ distinct roots; (ii) $i(\Pc, n)$ possesses exactly $2k$ imaginary roots; (iii) $i(\Pc, n)$ possesses exactly $d-2k$ real roots; (iv) the real part of each of the imaginary roots is equal to $-1/2$; (v) all of the real roots belong to the open interval $(-1,0)$.

6 pages

References in corpus (1)

• Gale duality bounds for roots of polynomials with nonnegative coefficients

Cited by in corpus (4)

• Reflexive polytopes of higher index and the number 12
• Roots of Ehrhart Polynomials of Smooth Fano Polytopes
• Gorenstein matroids
• Gorenstein graphic matroids