Discrete mathematics, 2011-05, Vol.311 (8), p.634-644
2011
Details
- Autor(en) / Beteiligte
- Titel
- Notes on lattice points of zonotopes and lattice-face polytopes
- Ist Teil von
- Discrete mathematics, 2011-05, Vol.311 (8), p.634-644
- Ort / Verlag
- Kidlington: Elsevier B.V
- Erscheinungsjahr
- 2011
- Link zum Volltext
- Quelle
- Alma/SFX Local Collection
- Beschreibungen/Notizen
- 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.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0012-365XeISSN: 1872-681XDOI: 10.1016/j.disc.2011.01.006Titel-ID: cdi_proquest_miscellaneous_864446532
- Format
- –
- Schlagworte
- Algebra, Combinatorics, Combinatorics. Ordered structures, Convex and discrete geometry, Ehrhart polynomial, Exact sciences and technology, Geometry, Lattice-face polytope, Lattices, Mathematical analysis, Mathematics, Minima, Order, lattices, ordered algebraic structures, Parallelepipeds, Polytopes, Sciences and techniques of general use, Successive minima, Theorems, Upper bounds, Zonotope