On the general no-three-in-line problem
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866911585311653888 |
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| author | Agama, Theophilus |
| author_facet | Agama, Theophilus |
| contents | In this paper, we show that the number of points that can be placed in the grid $n\times n\times \cdots \times n~(d~times)=n^d$ for all $d\in \mathbb{N}$ with $d\geq 2$ so that no three points are collinear satisfies the lower bound \begin{align} \gg n^{d-1}\sqrt[2d]{d}.\nonumber \end{align} This extends the result of the no-three-in-line problem to all dimension $d\geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_15621 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the general no-three-in-line problem Agama, Theophilus Combinatorics Metric Geometry 52C10, 52C35 In this paper, we show that the number of points that can be placed in the grid $n\times n\times \cdots \times n~(d~times)=n^d$ for all $d\in \mathbb{N}$ with $d\geq 2$ so that no three points are collinear satisfies the lower bound \begin{align} \gg n^{d-1}\sqrt[2d]{d}.\nonumber \end{align} This extends the result of the no-three-in-line problem to all dimension $d\geq 3$. |
| title | On the general no-three-in-line problem |
| topic | Combinatorics Metric Geometry 52C10, 52C35 |
| url | https://arxiv.org/abs/2106.15621 |