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Geometric permutations of disjoint unit spheres
- Issue Date
- Mar-2005
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- geometric permutation; line transversal; unit sphere; unit ball; Hadwiger-type theorem; Helly-type theorem
- Citation
- COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, v.30, no.3, pp.253 - 270
- Journal Title
- COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS
- Volume
- 30
- Number
- 3
- Start Page
- 253
- End Page
- 270
- ISSN
- 0925-7721
- Abstract
- We show that a set of n disjoint unit spheres in R(d) 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 R 3 : 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. (c) 2004 Elsevier B.V. All rights reserved.
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Related Researcher
- Na, Hyeon-Suk
- College of Information Technology (School of Computer Science and Engineering)