volume 34, issue 1, P1-10 2004
DOI: 10.1007/s00454-004-1110-x
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Abstract: 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.

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