Roots of Ehrhart Polynomials of Gorenstein Fano Polytopes
نویسندگان
چکیده
Abstract. Given arbitrary integers k and d with 0 ≤ 2k ≤ d, we construct a Gorenstein Fano polytope P ⊂ R of dimension d such that (i) its Ehrhart polynomial i(P , n) possesses d distinct roots; (ii) i(P , n) possesses exactly 2k imaginary roots; (iii) i(P , 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).
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