The Maximal Number of Geometric Permutations
for n Disjoint Translates of a Convex Set in ℝ Is Ω(n) |
| |
Authors: | Andrei Asinowski Meir Katchalski |
| |
Institution: | (1) Faculty of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel |
| |
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). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |