Distinct Distances with $\ell_p$ Spaces
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arXiv
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| Auteurs principaux: | , , , , , , , , , , , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866910627653484544 |
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| author | 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 |
| author_facet | 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 |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_05184 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Distinct Distances with $\ell_p$ Spaces 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 Combinatorics 05-02 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. |
| title | Distinct Distances with $\ell_p$ Spaces |
| topic | Combinatorics 05-02 |
| url | https://arxiv.org/abs/2010.05184 |