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
收藏
页码：70 / 83
页数：14
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