Geometric permutations of disjoint unit spheres

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Abstract

We show that a set of n disjoint unit spheres in Rd admits 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 in R3: 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.

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Cheong, O., Goaoc, X., & Na, H. S. (2005). Geometric permutations of disjoint unit spheres. Computational Geometry: Theory and Applications, 30(3), 253–270. https://doi.org/10.1016/j.comgeo.2004.08.003

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