## Abstract

We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls in ℝ^{d}, is Θ(n^{d-1}). This improves substantially the upper bound of O(n^{2d-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

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