Abstract
A geometric permutation induced by a transversal line of a finite family of disjoint convex sets in ℝd is the order in which the transversal meets the members of the family. It is known that the maximal number of geometric permutations in families of n disjoint translates of a convex set in ℝ3 is 3. We prove that for d ≥ 3 the maximal number of geometric permutations for such families in ℝd is Ω(n).
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Asinowski, A., Katchalski, M. The Maximal Number of Geometric Permutations for n Disjoint Translates of a Convex Set in ℝ Is Ω(n). Discrete Comput Geom 35, 473–480 (2006). https://doi.org/10.1007/s00454-005-1219-6
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DOI: https://doi.org/10.1007/s00454-005-1219-6