Abstract
We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls in ℝd, is Θ(nd-1). This improves substantially the upper bound of O(n2d-2) known for general convex sets [9]. We show that the maximum number of geometric permutations of a sufficiently large collection of pairwise disjoint unit disks in the plane is two, improving the previous upper bound of three given in [5].
Original language | English |
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Pages (from-to) | 247-259 |
Number of pages | 13 |
Journal | Discrete and Computational Geometry |
Volume | 23 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jan 2000 |
Externally published | Yes |
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics