Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Ghosal, Anubhab
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Clarendon Fund
OpenAlex ID: W7160858433
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