Smooth Fano Polytopes Whose Ehrhart Polynomial Has a Root with Large Real Part

被引：0

作者：

Hidefumi Ohsugi

Kazuki Shibata

机构：

[1] Rikkyo University,Department of Mathematics, College of Science

来源：

Discrete & Computational Geometry | 2012年 / 47卷

关键词：

Ehrhart polynomials; Gröbner bases; Gorenstein Fano polytopes;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：624 / 628

页数：4

共 11 条

[1] Smooth Fano Polytopes Whose Ehrhart Polynomial Has a Root with Large Real Part
Ohsugi, Hidefumi
Shibata, Kazuki
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2012, 47 (03) : 624 - 628
[2] Roots of Ehrhart Polynomials of Smooth Fano Polytopes
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Kasprzyk, Alexander M.
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2011, 46 (03) : 488 - 499
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