Lower bounds on the coefficients of Ehrhart polynomials

被引：19

作者：

Henk, Martin ^{[1
]}

Tagami, Makoto ^{[1
]}

机构：

[1] Univ Magdeburg, Inst Algebra & Geometrie, D-39106 Magdeburg, Germany

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2009年 / 30卷 / 01期

基金：

日本学术振兴会;

关键词：

GEOMETRIE DIOPHANTIENNE; ROOTS;

D O I：

10.1016/j.ejc.2008.02.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present lower bounds for the coefficients of Ehrhart polynomials of convex lattice polytopes in terms of their volume. Concerning the coefficients of the Ehrhart series of a lattice polytope we show that Hibi's lower bound is not true for lattice polytopes without interior lattice points. The counterexample is based on a formula of the Ehrhart series of the join of two lattice polytope. We also present a formula for calculating the Ehrhart series of integral dilates of a polytope. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：70 / 83

页数：14

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