论文标题
$ \ ell_p $ spaces的独特距离
Distinct Distances with $\ell_p$ Spaces
论文作者
论文摘要
我们研究Erd \ h OS在$ \ ell_p $ cum $ p $下方的距离问题下的独特距离问题。对于任何$ε> 0 $，我们将目前的最佳绑定从$ω（n^{4/5}）$提高到$ω（n^{6/7-ε}）$。我们还表征了跨越$ \ ell_1 $和$ \ ell_ \ eld_ \ infty $指标下渐近数量的不同距离的集合。
We study Erd\H os's distinct distances problem under $\ell_p$ metrics with integer $p$. We improve the current best bound for this problem from $Ω(n^{4/5})$ to $Ω(n^{6/7-ε})$, for any $ε>0$. We also characterize the sets that span an asymptotically minimal number of distinct distances under the $\ell_1$ and $\ell_\infty$ metrics.
