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arXiv · 2407.01174

A problem of Erdős about rich distances

Krishnendu Bhowmick
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Abstract

An old question posed by Erdős asked whether there exists a set of $n$ points such that $c \cdot n$ distances occur more than $n$ times. We provide an affirmative answer to this question, showing that there exists a set of $n$ points such that $\lfloor \frac{n}{4}\rfloor$ distances occur more than $n$ times. We also present a generalized version, finding a set of $n$ points where $c_m \cdot n$ distances occurring more than $n+m$ times.

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Krishnendu Bhowmick. 2024-07-04. A problem of Erdős about rich distances. https://arxiv.org/abs/2407.01174

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