Roots of Ehrhart Polynomials of Smooth Fano Polytopes

被引：3

作者：

Hegedues, Gabor ^{[1
]}

Kasprzyk, Alexander M. ^{[2
]}

机构：

[1] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, A-4040 Linz, Austria

[2] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2011年 / 46卷 / 03期

关键词：

Lattice polytope; Ehrhart polynomial; Nonsingular toric Fano; Canonical line hypothesis;

D O I：

10.1007/s00454-010-9275-y

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

V. Golyshev conjectured that for any smooth polytope P with dim(P)a parts per thousand currency sign5 the roots zaa", 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.

引用

页码：488 / 499

页数：12

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