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2011

Notes on lattice points of zonotopes and lattice-face polytopes

11 years 3 months ago
Notes on lattice points of zonotopes and lattice-face polytopes
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.
Christian Bey, Martin Henk, Matthias Henze, Eva Li
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where DM
Authors Christian Bey, Martin Henk, Matthias Henze, Eva Linke
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