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We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls inR d ,i s2.n di1 /. This improves substantially the upper bound of O.n 2di2 / 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).

Sharp bounds on geometric permutations of pairwise disjoint balls in R d

Sharp bounds on geometric permutations of pairwise disjoint balls in R ^d