论文标题
圆和通用集之间的独特距离
Distinct Distances Between a Circle and a Generic Set
论文作者
论文摘要
令$ s $为$ \ mathbb {r}^2 $中包含的一组点，而$ p $ $ \ mathbb {r}^2 $中的无限制点设置为。我们证明了$ s $中点之间的不同距离的数量，$ p $中的点至少为$ \ min（| s || p |^{1/4- \ varepsilon}，| s | s |^{2/3} | p |^{2/3} {2/3}，| s |^2，|^2，| p |^2）$。 这是建立在Pach和de Zeeuw，Bruner和Sharir，McLaughlin和Omar和Mathialagan之间的作品的基础上的。
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.
