Geometric permutations of disjoint unit spheres

  • Cheong O
  • Goaoc X
  • Na H
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Abstract

We show that a set of n disjoint unit spheres inRdadmits at most two distinct geometric permutations if n≥9, and at most three if 3≤n≤8. This result improves a Helly-type theorem on line transversals for disjoint unit spheres inR3: if any subset of size at most 18 of a family of such spheres admits a line transversal, then there is a line transversal for the entire family. © 2004 Elsevier B.V.

Author-supplied keywords

  • Geometric permutation
  • Hadwiger-type theorem
  • Helly-type theorem
  • Line transversal
  • Unit ball
  • Unit sphere

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Authors

  • Otfried Cheong

  • Xavier Goaoc

  • Hyeon Suk Na

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