Notes on lattice points of zonotopes and lattice-face polytopes
Metric Geometry
2010-11-09 v2 Combinatorics
Abstract
Minkowski's second theorem on successive minima gives an upper bound on the volume of a convex body in terms of its successive minima. We study the problem to generalize Minkowski's bound by replacing the volume by the lattice point enumerator of a convex body. In this context we are interested in bounds on the coefficients of Ehrhart polynomials of lattice polytopes via the successive minima. Our results for lattice zonotopes and lattice-face polytopes imply, in particular, that for 0-symmetric lattice-face polytopes and lattice parallelepipeds the volume can be replaced by the lattice point enumerator.
Keywords
Cite
@article{arxiv.1006.5574,
title = {Notes on lattice points of zonotopes and lattice-face polytopes},
author = {Christian Bey and Martin Henk and Matthias Henze and Eva Linke},
journal= {arXiv preprint arXiv:1006.5574},
year = {2010}
}
Comments
16 pages, incorporated referee remarks, corrected proof of Theorem 1.2, added new co-author