An incomplete attack on the upper bound of the unit distance problem

Steven Senger

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arXiv · 2605.26145

An incomplete attack on the upper bound of the unit distance problem

Steven Senger

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Abstract

This is an incomplete attempt to show that the upper bound of $\lesssim n^\frac{4}{3}$ on the number unit distances determined by a large finite set of $n$ points in the plane is not sharp. The methods also say something about sets of $n$ points and $n$ lines that attain the sharp bound of the Szemer\'edi-Trotter point-line incidence bound.

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Steven Senger. 2026-05-22. An incomplete attack on the upper bound of the unit distance problem. https://arxiv.org/abs/2605.26145

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