### Abstract

We answer the following question posed by Paul Erdős and George Purdy: determine the largest number f _{d} (k) = f with the property that almost all k-element subsets of any n-element set in R ^{d} determine at least f distinct distances, for all sufficiently large n. For d = 2 we investigate the asymptotic behaviour of the maximum number of k-element subsets of a set of n points, each subset determining at most i distinct distances, for some prespecified number i. We also show that if k = o(n ^{ 1 7} ), almost all k-element subsets of a planar point set determine distinct distances.

Original language | English |
---|---|

Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Computational Geometry: Theory and Applications |

Volume | 1 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 1991 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computational Geometry: Theory and Applications*,

*1*(1), 1-11. https://doi.org/10.1016/0925-7721(91)90009-4