Advertisement

Discrete & Computational Geometry

, Volume 35, Issue 4, pp 537–549 | Cite as

Distinct Distances in Homogeneous Sets in Euclidean Space

  • Jozsef Solymosi
  • Csaba D. Toth
Article

Abstract

It is shown that every homogeneous set of n points in d-dimensional Euclidean space determines at least \(\Omega(n^{2d/(d^2+1)} / \log^{c(d)} n)\) distinct distances for a constant c(d) > 0. In three-space the above general bound is slightly improved and it is shown that every homogeneous set of n points determines at least \(\Omega(n^{0.6091})\) distinct distances.

Keywords

Computational Mathematic Euclidean Space Distinct Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2Canada
  2. 2.Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139USA

Personalised recommendations