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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.07000 |
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Table of 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.