Coefficient inequality for a function whose derivative has a positive real part of order $\alpha $

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The symmetric edge polytopes of odd cycles (del Pezzo polytopes) are known as smooth Fano polytopes. In this extended abstract, 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. Résumé...

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ژورنال

عنوان ژورنال: Mathematica Bohemica

سال: 2015

ISSN: 0862-7959,2464-7136

DOI: 10.21136/mb.2015.144178