论文标题
单位距离问题的提高了常数因素
An improved constant factor for the unit distance problem
论文作者
论文摘要
我们证明，$ n $平面点之间的单位距离数量最多为$ 1.94 \ cdot n^{4/3} $，在先前的$ 8N^{4/3} $的最佳限制上有所改善。我们还为$ n $的几个小值提供了更好的上限和下限。我们还证明了交叉引理的某些变体并改善了一些恒定因素。
We prove that the number of unit distances among $n$ planar points is at most $1.94\cdot n^{4/3}$, improving on the previous best bound of $8n^{4/3}$. We also give better upper and lower bounds for several small values of $n$. We also prove some variants of the crossing lemma and improve some constant factors.
