, Volume 28, Issue 1, pp 113-125

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

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Abstract

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 ).