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TitleSmooth Fano polytopes whose Ehrhart polynomial has a root with large real part.
Author(s) Hidefumi Ohsugi, Kazuki Shibata
TypeArticle in Journal
AbstractThe 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.
KeywordsEhrhart polynomials, Gröbner bases, Gorenstein, Fano polytopes
ISSN0179-5376; 1432-0444/e
URL http://link.springer.com/article/10.1007%2Fs00454-012-9395-7
LanguageEnglish
JournalDiscrete Comput. Geom.
Volume47
Number3
Pages624--628
PublisherSpringer US, New York, NY
Year2012
Edition0
Translation No
Refereed No
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