Combinatorica

, Volume 28, Issue 1, pp 113–125 | Cite as

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

Article

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 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

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

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