Geometric permutations of disjoint unit spheres
Identifieur interne : 000135 ( Crin/Checkpoint ); précédent : 000134; suivant : 000136Geometric permutations of disjoint unit spheres
Auteurs : Otfried Cheong ; Xavier Goaoc ; Hyeon-Suk NaSource :
- Computational Geometry : Theory and Applications ; 2005.
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Abstract
We show that a set of n disjoint unit spheres in R^d admits at most two distinct geometric permutations if n > 8, and at most three if 2 < n < 9. This result improves a Helly-type theorem on line transversals for disjoint unit spheres in R^3 : if any subset of size 18 of a family of such spheres admits a line transversal, then there is a line transversal for the entire family.
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