A note on the extensible no-three-in-line problem
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914542699675648 |
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| author | Ghosal, Anubhab |
| author_facet | Ghosal, Anubhab |
| contents | We show the existence of a set $S\subset\mathbb{Z}^2$ avoiding collinear triples satisfying $|S\cap [n]^2|=Ω(n/\sqrt{\log n})$ for sufficiently large $n$. This improves on the best-known lower bound on Erde's extensible no-three-in-line problem due to Nagy, Nagy and Woodroofe by $\sqrt{\log n}$, leaving the same gap to the trivial upper bound. Our construction is random. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07000 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on the extensible no-three-in-line problem Ghosal, Anubhab Combinatorics 05D40, 52C35 We show the existence of a set $S\subset\mathbb{Z}^2$ avoiding collinear triples satisfying $|S\cap [n]^2|=Ω(n/\sqrt{\log n})$ for sufficiently large $n$. This improves on the best-known lower bound on Erde's extensible no-three-in-line problem due to Nagy, Nagy and Woodroofe by $\sqrt{\log n}$, leaving the same gap to the trivial upper bound. Our construction is random. |
| title | A note on the extensible no-three-in-line problem |
| topic | Combinatorics 05D40, 52C35 |
| url | https://arxiv.org/abs/2605.07000 |