Forbidden Families of Geometric Permutations in ℝ^d

A geometric permutation induced by a transversal line of a finite family ℱ of disjoint convex sets in ℝ^d 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 ℝ^d for d ≥ 2k – 1, but there is a family of k permutations which is non-realizable in ℝ^d for d ≤ 2k – 2.

Authors and Affiliations

1. Faculty of Mathematics, Technion–Israel Institute of Technology, Haifa 32000, Israel

   Andrei Asinowski & Meir Katchalski

Corresponding authors

Correspondence to Andrei Asinowski or Meir Katchalski.

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