Abstract
A geometric permutation induced by a transversal line of a finite family ℱ of disjoint convex sets in ℝd is the order in which the transversal meets the members of the family. We prove that for each natural k, each family of k permutations is realizable (as a family of geometric permutations of some ℱ) in ℝd for d ≥ 2k – 1, but there is a family of k permutations which is non-realizable in ℝd for d ≤ 2k – 2.
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