Forbidden Families of Geometric Permutations in ℝd

  • Authors:

  • Andrei Asinowski;Meir Katchalski

  • Affiliations:

  • Faculty of Mathematics, Technion–Israel Institute of Technology, Haifa 32000, Israel;Faculty of Mathematics, Technion–Israel Institute of Technology, Haifa 32000, Israel

  • Venue:
  • Discrete & Computational Geometry
  • Year:
  • 2005

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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.