Ehrhart polynomials and successive minima
By Martin Henk, A. Schuermann, J. M. Wills. 2005
54 citations recorded by the source corpus.
We investigate the Ehrhart polynomial for the class of 0-sym- metric convex lattice polytopes in Euclidean n-space 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.
Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/27e3781afd76fc2e69e7091f9e40a7b7912eb777
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In Applied Mathematics
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Cone-volume measure of general centered convex bodies (2016, unknown): “Wills [24] and B.”
- Roots of Ehrhart polynomials arising from graphs (2010, unknown): “Among the many papers on the topic, including [4], [5], [6], [12] and [23], Beck et al.”
- Cone-volume measures of polytopes (2013, background): “in the special case dimL = 1 by Hernandez Cifre (2007, private communication), in the cases dimL = 1,n−1 by Xiong [29], and for originsymmetric polytopes independently by Henk, Schu¨rmann & Wills [14] and by He, Leng & Li [13]. The motivation for studying the relation (1.3) for the class of ”