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arXiv · 2005.02951

Distinct Distances Between a Circle and a Generic Set

Alex McDonald·Brian McDonald·Jonathan Passant·Anurag Sahay
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Abstract

Let $S$ be a set of points in $\mathbb{R}^2$ contained in a circle and $P$ an unrestricted point set in $\mathbb{R}^2$. We prove the number of distinct distances between points in $S$ and points in $P$ is at least $\min(|S||P|^{1/4-\varepsilon},|S|^{2/3}|P|^{2/3},|S|^2,|P|^2)$. This builds on work of Pach and De Zeeuw, Bruner and Sharir, McLaughlin and Omar and Mathialagan on distances between pairs of sets.

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Alex McDonald, Brian McDonald, Jonathan Passant, Anurag Sahay. 2020-05-06. Distinct Distances Between a Circle and a Generic Set. https://arxiv.org/abs/2005.02951

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