, Volume 28, Issue 1, pp 113-125
Date: 29 Apr 2008

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

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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