Roots of Ehrhart Polynomials of Smooth Fano Polytopes

Details Roots of Ehrhart Polynomials of Smooth Fano Polytopes Roots of Ehrhart Polynomials of Smooth Fano Polytopes

2010-04-21

arxiv.org/abs/1004.3817v1

Mathematics

Combinatorics

10 pages

Scientific paper

10.1007/s00454-010-9275-y

V. Golyshev conjectured that for any smooth polytope P of dimension at most
five, the roots $z\in\C$ of the Ehrhart polynomial for P have real part equal
to -1/2. An elementary proof is given, and in each dimension the roots are
described explicitly. We also present examples which demonstrate that this
result cannot be extended to dimension six.

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