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. We show that the maximum number of geometric permutations of a sufficiently large collection of pair-wise disjoint unit discs in the plane is 2, improving the previous upper bound of 3 given in [5].