Highly saturated packings and reduced coverings

DOI10.1007/BF01332823zbMath0901.52020arXivmath/9511225MaRDI QIDQ1383738

D. Massart

Publication date: 26 April 1998

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

Full work available at URL: https://arxiv.org/abs/math/9511225

zbMATH Keywords

packingsaturatedcoveringsEuclidean \(d\)-spacedensity boundshyperbolic \(d\)-space

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Combinatorial aspects of packing and covering (05B40)

Related Items (17)

Top dense hyperbolic ball packings and coverings for complete coxeter orthoscheme groups ⋮ Horoball packings to the totally asymptotic regular simplex in the hyperbolic \(n\)-space ⋮ Congruent and non-congruent hyperball packings related to doubly truncated Coxeter orthoschemes in hyperbolic 3-space ⋮ Hyperball packings in hyperbolic $3$-space ⋮ Packing Coxeter honeycombs with sequences of spheres ⋮ An upper bound of the density for packing of congruent hyperballs in hyperbolic \(3\)-space ⋮ A candidate for the densest packing with equal balls in Thurston geometries ⋮ Packings with horo- and hyperballs generated by simple frustum orthoschemes ⋮ Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types ⋮ New lower bound for the optimal ball packing density in hyperbolic 4-space ⋮ Density upper bound for congruent and non-congruent hyperball packings generated by truncated regular simplex tilings ⋮ The least dense hyperball covering of regular prism tilings in hyperbolic \(n\)-space ⋮ Decomposition method related to saturated hyperball packings ⋮ Saturated packings and reduced coverings obtained by perturbing tilings ⋮ Notions of denseness ⋮ Horoball packings related to the 4-dimensional hyperbolic 24 cell honeycomb {3,4,3,4} ⋮ Hyperball packings related to truncated cube and octahedron tilings in hyperbolic space

Cites Work

• The difference body of a convex body
• Disks with special properties of densest packings
• An extension of the Erdős-Szekeres theorem on large angles
• Lectures on hyperbolic geometry
• Compact Clifford-Klein forms of symmetric spaces
• Existenzsätze für Lagerungen im Euklidischen Raum
• A note on coverings
• The Packing of Equal Spheres
• Covering space with equal spheres
• Packing of spheres in spaces of constant curvature
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