Roots of Ehrhart polynomials of Gorenstein Fano polytopes

Hibi, Takayuki; Higashitani, Akihiro; Ohsugi, Hidefumi

doi:10.1090/S0002-9939-2011-11013-X

Roots of Ehrhart polynomials of Gorenstein Fano polytopes
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by Takayuki Hibi, Akihiro Higashitani and Hidefumi Ohsugi PDF

Proc. Amer. Math. Soc. 139 (2011), 3727-3734 Request permission

Abstract:

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

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