No‐(k+1)‐in‐line problem for large constant k Grebennikov, Aleksandr Kwan, Matthew Alan ; https://orcid.org/0000-0002-4003-7567 ddc:510 How many points can be placed in an 𝑛 × 𝑛 grid sothat every (affine) line contains at most 𝑘 points? Weprove that for 𝑛 ⩾ 𝑘 ⩾ 1037 the maximum number ofpoints is exactly 𝑘𝑛. Our proof builds on the recent workof Kovács, Nagy and Szabó (who proved an analogousresult when 𝑘 is at least about √𝑛 log 𝑛), incorporat-ing ideas of Jain and Pham. Using the same approach,we also obtain new bounds for higher-dimensionalextensions of this problem Wiley 2026 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/23123 https://research-explorer.ista.ac.at/download/23123/23139 Grebennikov A, Kwan MA. No‐(k+1)‐in‐line problem for large constant k. <i>Bulletin of the London Mathematical Society</i>. 2026;58(10). doi:<a href="https://doi.org/10.1112/blms.70510">10.1112/blms.70510</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1112/blms.70510 info:eu-repo/semantics/altIdentifier/issn/0024-6093 info:eu-repo/semantics/altIdentifier/e-issn/1469-2120 info:eu-repo/semantics/openAccess