Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.10509 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915615849054208 |
|---|---|
| author | Logunov, Alexander Zakharov, Dmitrii |
| author_facet | Logunov, Alexander Zakharov, Dmitrii |
| contents | We show that for every $n \in \mathbb N$ there is a collection of points $p_1, \ldots, p_n$ and lines $\ell_1, \ldots, \ell_n$ in the unit square such that for any $i$ we have $p_i \in \ell_i$ and the distance from $p_i$ to any other line $\ell_j$ is at least $c n^{γ-1}$ for some universal constants $c, γ>0$. This is better than a trivial construction by a polynomial factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A fractal-like configuration of point-line pairs for the minimal distance problem Logunov, Alexander Zakharov, Dmitrii Combinatorics We show that for every $n \in \mathbb N$ there is a collection of points $p_1, \ldots, p_n$ and lines $\ell_1, \ldots, \ell_n$ in the unit square such that for any $i$ we have $p_i \in \ell_i$ and the distance from $p_i$ to any other line $\ell_j$ is at least $c n^{γ-1}$ for some universal constants $c, γ>0$. This is better than a trivial construction by a polynomial factor. |
| title | A fractal-like configuration of point-line pairs for the minimal distance problem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.10509 |