Maximum number of points in general position in a random subset of finite $3$-dimensional spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915728735600640 |
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| author | Balogh, József Luo, Haoran |
| author_facet | Balogh, József Luo, Haoran |
| contents | Let $α(\mathbb{F}_q^{d},p)$ be the maximum possible size of a point set in general position in the $p$-random subset of $\mathbb{F}_q^d$. In this note, we determine the order of magnitude of $α(\mathbb{F}_q^{3},p)$ up to a polylogarithmic factor by proving a balanced supersaturation result for the sets of $4$ points in the same plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04102 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum number of points in general position in a random subset of finite $3$-dimensional spaces Balogh, József Luo, Haoran Combinatorics Probability 05B25, 05C80, 05C65 Let $α(\mathbb{F}_q^{d},p)$ be the maximum possible size of a point set in general position in the $p$-random subset of $\mathbb{F}_q^d$. In this note, we determine the order of magnitude of $α(\mathbb{F}_q^{3},p)$ up to a polylogarithmic factor by proving a balanced supersaturation result for the sets of $4$ points in the same plane. |
| title | Maximum number of points in general position in a random subset of finite $3$-dimensional spaces |
| topic | Combinatorics Probability 05B25, 05C80, 05C65 |
| url | https://arxiv.org/abs/2503.04102 |