Erdős Distance Problem in ℝ^d

2020/02/04 by Esen Aksoy Yazici, Yazici, Esen Aksoy
Mathematics · #Limits and Structures in Graph Theory #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2002.01248

Abstract

In this paper, we prove Erdős distance conjecture in ℝ^d, namely, a set of n points in ℝ² determines Ω((n)/(√(log n))) distances, and for d≥ 3, a set of n points in ℝ^d determines Ω(n^(2)/(d)) distinct distances.

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