Geometric permutations of non-overlapping unit balls revisited

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Given four congruent balls A, B, C, D in R-delta that have disjoint interior and admit a line that intersects them in the order ABCD, we show that the distance between the centers of consecutive balls is smaller than the distance between the centers of A and D. This allows us to give a new short proof that n interior-disjoint congruent balls admit at most three geometric permutations, two if n >= 7. We also make a conjecture that would imply that n >= 4 such balls admit at most two geometric permutations, and show that if the conjecture is false, then there is a counter-example that is algebraically highly degenerate. (C) 2015 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2016-02
Language
English
Article Type
Article
Keywords

LINE TRANSVERSALS; CONVEX-SETS; R-D; SPHERES; FAMILIES; NUMBER; BOUNDS

Citation

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, v.53, pp.36 - 50

ISSN
0925-7721
DOI
10.1016/j.comgeo.2015.12.003
URI
http://hdl.handle.net/10203/219685
Appears in Collection
CS-Journal Papers(저널논문)
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