Sharp bounds on geometric permutations of pairwise disjoint balls in R d Academic Article uri icon


  • Abstract We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls in IRd, is O (nd-l). This improves substantially the upper bound of O (n2d-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 discs in the plane is 2, improving the previous upper bound of 3 given in [5].

publication date

  • January 1, 2000