Abstract.
We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls in \R d , is Θ (n d-1 ) . This improves substantially the upper bound of O(n 2d-2 ) known for general convex sets [9].
We show that the maximum number of geometric permutations of a sufficiently large collection of pairwise disjoint unit disks in the plane is two, improving the previous upper bound of three given in [5].
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Received September 21, 1998, and in revised form March 14, 1999.
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Smorodinsky, S., Mitchell, J. & Sharir, M. Sharp Bounds on Geometric Permutations of Pairwise Disjoint Balls in R d . Discrete Comput Geom 23, 247–259 (2000). https://doi.org/10.1007/PL00009498
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DOI: https://doi.org/10.1007/PL00009498