### Abstract

Given a finite set of complex numbers A we say that a transformation on the complex numbers, T: C → C is k-rich on A if |A T(A)| k. In this paper we give a bounds on the number of k-rich linear and Möbius transformations for any given set A. Our results have applications to discrete geometry and to additive combinatorics.

Original language | English |
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Title of host publication | Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07 |

Pages | 227-231 |

Number of pages | 5 |

DOIs | |

Publication status | Published - Oct 22 2007 |

Event | 23rd Annual Symposium on Computational Geometry, SCG'07 - Gyeongju, Korea, Republic of Duration: Jun 6 2007 → Jun 8 2007 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
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### Other

Other | 23rd Annual Symposium on Computational Geometry, SCG'07 |
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Country | Korea, Republic of |

City | Gyeongju |

Period | 6/6/07 → 6/8/07 |

### Keywords

- Möbius transformation
- Point-line incidences

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

Solymosi, J., & Tardos, G. (2007). On the number of k-rich transformations. In

*Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07*(pp. 227-231). (Proceedings of the Annual Symposium on Computational Geometry). https://doi.org/10.1145/1247069.1247111