Erd\H{o}s Distance Problem in $\mathbb{R}^d$

Esen Aksoy Yazici

Erd\H{o}s Distance Problem in $\mathbb{R}^d$

Combinatorics 2020-02-13 v3 Number Theory

Authors: Esen Aksoy Yazici

Abstract

In this paper, we prove Erd\H{o}s distance conjecture in $\mathbb{R}^d$ , namely, a set of $n$ points in $\mathbb{R}^2$ determines $\Omega(\frac{n}{\sqrt{\log n}})$ distances, and for $d\ge 3$ , a set of $n$ points in $\mathbb{R}^d$ determines $\Omega(n^{\frac{2}{d}})$ distinct distances.

Keywords

distance sets euclidean distance and geometry

Cite

@article{arxiv.2002.01248,
  title  = {Erd\H{o}s Distance Problem in $\mathbb{R}^d$},
  author = {Esen Aksoy Yazici},
  journal= {arXiv preprint arXiv:2002.01248},
  year   = {2020}
}

Comments

The paper is withdrawn as the proof of Theorem 1.2 is not correct

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