An application of valuation theory to two problems in discrete geometry

DOI10.1016/0012-365X(86)90188-3zbMath0596.52013OpenAlexW2000272149MaRDI QIDQ1078811

Peter Gritzmann, Ulrich. Betke

Publication date: 1986

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(86)90188-3

zbMATH Keywords

convex polytopeslattice point enumeratorL. Fejes-Tóth sausage-conjecturelattice zonotopepackings of the unit ballsimple valuation

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattices and convex bodies (number-theoretic aspects) (11H06) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Polytopes and polyhedra (52Bxx)

Related Items

An upper estimate for the lattice point enumerator, $h^\ast $-polynomials of zonotopes, Notes on lattice points of zonotopes and lattice-face polytopes, Minkowski's successive minima and the zeros of a convexity-function, Ehrhart Polynomials and Successive Minima, The sausage conjecture holds for convex hulls of moderately bent sausages

Cites Work

• Zur Gitterpunktanzahl konvexer Mengen
• Slices of L. Fejes Tóth's sausage conjecture
• Non-linear angle-sum relations for polyhedral cones and polytopes
• Valuations and Euler-Type Relations on Certain Classes of Convex Polytopes
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