On the number of k-rich transformations

Jozsef Solymosi, Gabor Tardos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

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 languageEnglish
Title of host publicationProceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07
Pages227-231
Number of pages5
DOIs
Publication statusPublished - Oct 22 2007
Event23rd Annual Symposium on Computational Geometry, SCG'07 - Gyeongju, Korea, Republic of
Duration: Jun 6 2007Jun 8 2007

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Other

Other23rd Annual Symposium on Computational Geometry, SCG'07
CountryKorea, Republic of
CityGyeongju
Period6/6/076/8/07

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