Geometric permutations of non-overlapping unit balls revisited

DOI10.1016/j.comgeo.2015.12.003zbMath1337.51006arXiv1407.0795OpenAlexW2215190454MaRDI QIDQ265727

Jungwoo Yang, Jae-Soon Ha, Xavier Goaoc, Otfried Schwarzkopf

Publication date: 12 April 2016

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0795

zbMATH Keywords

unit ballgeometric permutationcongruent ballsline transversaltransversal theory

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Other designs, configurations (05B30) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Euclidean geometries (general) and generalizations (51M05)

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Cites Work

• Lines pinning lines
• The maximum number of ways to stab n convex nonintersecting sets in the plane is 2n-2
• Common tangents to spheres in \(\mathbb R^{3}\)
• Geometric permutations of disjoint translates of convex sets
• A Helly-type theorem for line transversals to disjoint unit balls
• Lower bounds to Helly numbers of line transversals to disjoint congruent balls
• Geometric permutations of disjoint unit spheres
• Sharp bounds on geometric permutations of pairwise disjoint balls in \(\mathbb{R}^d\)
• Geometric permutations for convex sets
• Line transversals to disjoint balls
• Helly-type theorems for line transversals to disjoint unit balls
• The envelope of lines meeting a fixed line and tangent to two spheres
• Improved Bounds for Geometric Permutations
• Common Secants for Plane Convex Sets
• Algorithms in real algebraic geometry
• A tight bound on the number of geometric permutations of convex fat objects in \(\mathbb{R}^d\)
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