Intrinsic volumes and lattice points of crosspolytopes

DOI10.1007/BF01311208zbMath0779.52013MaRDI QIDQ1261140

Martin Henk, Ulrich. Betke

Publication date: 16 September 1993

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178596

zbMATH Keywords

lattice polytopesintrinsic volumescrosspolytopes

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Mixed volumes and related topics in convex geometry (52A39)

Related Items (16)

Covering functionals of convex polytopes with few vertices ⋮ Algorithms for computing mixed multiplicities, mixed volumes, and sectional Milnor numbers ⋮ Small-ball probabilities for the volume of random convex sets ⋮ Intrinsic volumes and successive radii ⋮ Approximate CVP_p in Time 2^{0.802 n} ⋮ Further inequalities for the (generalized) Wills functional ⋮ Notes on the roots of Steiner polynomials ⋮ A Ronkin type function for coamoebas ⋮ Expected volumes of Gaussian polytopes, external angles, and multiple order statistics ⋮ Approximate CVP\(_p\) in time \(2^{0.802n}\) ⋮ On the roots of generalized Wills \(\mu\)-polynomials ⋮ A Blichfeldt-type inequality for the surface area ⋮ Gaussian convex bodies: a nonasymptotic approach ⋮ Absorption probabilities for Gaussian polytopes and regular spherical simplices ⋮ Monotonicity of expected 𝑓-vectors for projections of regular polytopes ⋮ The packing density of the \(n\)-dimensional cross-polytope

Cites Work

• On the geometrical moments of skew-regular simplices in hyperspherical space, with some applications in geometry and mathematical statistics
• An inequality relating volume, area and number of lattice points of convex sets in \(n\)-dimensional Euclidean space
• Zur Gitterpunktanzahl konvexer Mengen
• Non-linear angle-sum relations for polyhedral cones and polytopes
• Évaluation de la différence entre l'aire d'une région plane convexe et le nombre des points aux coordonnées entières couverts par elle
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