Combinatorica

, Volume 28, Issue 1, pp 113–125

Near optimal bounds for the Erdős distinct distances problem in high dimensions

Article

DOI: 10.1007/s00493-008-2099-1

Cite this article as:
Solymosi, J. & Vu, V.H. Combinatorica (2008) 28: 113. doi:10.1007/s00493-008-2099-1

Abstract

We show that the number of distinct distances in a set of n points in ℝd is Ω(n2/d − 2 / d(d + 2)), d ≥ 3. Erdős’ conjecture is Ω(n2/d).

Mathematics Subject Classification (2000)

52C10

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsUBCVancouverCanada
  2. 2.Department of Mathematics RutgersPiscatawayUSA