Shakhar Smorodinsky

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].