Distinct Distances with $\ell_p$ Spaces
| Autor: | 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 |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Computational Geometry Vol. 100, January 2022, 101785 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.comgeo.2021.101785 |
| Popis: | 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 $\Omega(n^{4/5})$ to $\Omega(n^{6/7-\epsilon})$, for any $\epsilon>0$. We also characterize the sets that span an asymptotically minimal number of distinct distances under the $\ell_1$ and $\ell_\infty$ metrics. Comment: 15 pages, 4 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|