arXiv math/05075282005-07-26math.MGmath.CO

Ehrhart polynomial and Successive Minima

Martin Henk, Achill Schuermann, Joerg M. Wills

发表信息：: Mathematika 52 (2005), 1-16
DOI：: 10.1112/S0025579300000292

英文摘要：

We investigate the Ehrhart polynomial for the class of 0-symmetric convex lattice polytopes in Euclidean $n$-space $\mathbb{R}^n$. It turns out that the roots of the Ehrhart polynomial and Minkowski's successive minima are closely related by their geometric and arithmetic mean. We also show that the roots of lattice $n$-polytopes with or without interior lattice points differ essentially. Furthermore, we study the structure of the roots in the planar case. Here it turns out that their distribution reflects basic properties of lattice polygons.

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