On infinite sets with no $3$ on a line
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911467179081728 |
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| author | Putterman, Moe Sawhney, Mehtaab Valiant, Gregory |
| author_facet | Putterman, Moe Sawhney, Mehtaab Valiant, Gregory |
| contents | We give a construction of an infinite set of points $A$ in $\mathbb{R}^2$ such that any subset $P\subseteq A$ has a constant density subset $P'$ with no three points collinear and yet $A$ cannot be separated into finitely many subsets such that each subset has no three points collinear. This provides a new proof of a question of Erdős, Nešetřil, and Rödl. The construction was generated by an internal model at OpenAI. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21275 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On infinite sets with no $3$ on a line Putterman, Moe Sawhney, Mehtaab Valiant, Gregory Combinatorics We give a construction of an infinite set of points $A$ in $\mathbb{R}^2$ such that any subset $P\subseteq A$ has a constant density subset $P'$ with no three points collinear and yet $A$ cannot be separated into finitely many subsets such that each subset has no three points collinear. This provides a new proof of a question of Erdős, Nešetřil, and Rödl. The construction was generated by an internal model at OpenAI. |
| title | On infinite sets with no $3$ on a line |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.21275 |