Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part

Details Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part

2011-09-05

arxiv.org/abs/1109.0791v2

Mathematics

Combinatorics

4 pages, We changed the order of the auhors and omitted a lot of parts of the paper. (If you are interested in omitted parts,

Scientific paper

The symmetric edge polytopes of odd cycles (del Pezzo polytopes) are known as
smooth Fano polytopes. In this paper, we show that if the length of the cycle
is 127, then the Ehrhart polynomial has a root whose real part is greater than
the dimension. As a result, we have a smooth Fano polytope that is a
counterexample to the two conjectures on the roots of Ehrhart polynomials.

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