Abstract
We show that the maximum number of geometric permutations of a set of n pairwise-disjoint convex and fat objects in R d is O(n d-1 ) . This generalizes the bound of Θ (n d-1 ) obtained by Smorodinsky et al. [5] on the number of geometric permutations of n pairwise-disjoint balls.
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Received August 22, 2000, and in revised form February 6, 2001. Online publication October 12, 2001.
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Katz, M., Varadarajan, K. A Tight Bound on the Number of Geometric Permutations of Convex Fat Objects in R d . Discrete Comput Geom 26, 543–548 (2001). https://doi.org/10.1007/s00454-001-0044-9
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DOI: https://doi.org/10.1007/s00454-001-0044-9