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Bibliographic Details
Main Authors:	AlQady, Moaaz, Chabot, Riley, Dudarov, William, Ge, Linus, Juvekar, Mandar, Kundeti, Srikanth, Kundu, Neloy, Lu, Kevin, Moreno, Yago, Peng, Sibo, Speas, Samuel, Starzycka, Julia, Steinthal, Henry, Vitko, Anastasiia
Format:	Preprint
Published:	2020
Subjects:	Combinatorics 05-02
Online Access:	https://arxiv.org/abs/2010.05184
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Table of Contents:

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.