article published yes Aleksandr Grebennikov author 776468ec-50b0-11ef-861e-96ad19e894f3 Matthew Alan Kwan author 5fca0887-a1db-11eb-95d1-ca9d5e0453b30000-0002-4003-7567 MaKw department GradSch department Randomness and structure in combinatorics project 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 https://research-explorer.ista.ac.at/download/23123/23139/2026_BulletinLondonMathSoc_Grebennikov.pdf application/pdfno Wiley2026 eng 0024-6093 1469-212010.1112/blms.70510 5810 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> Grebennikov A, Kwan MA. 2026. No‐(k+1)‐in‐line problem for large constant k. Bulletin of the London Mathematical Society. 58(10), e70510. Grebennikov, Aleksandr, and Matthew Alan Kwan. “No‐(K+1)‐in‐line Problem for Large Constant K.” <i>Bulletin of the London Mathematical Society</i>, vol. 58, no. 10, e70510, Wiley, 2026, doi:<a href="https://doi.org/10.1112/blms.70510">10.1112/blms.70510</a>. Grebennikov, A., &#38; Kwan, M. A. (2026). No‐(k+1)‐in‐line problem for large constant k. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href="https://doi.org/10.1112/blms.70510">https://doi.org/10.1112/blms.70510</a> A. Grebennikov, M.A. Kwan, Bulletin of the London Mathematical Society 58 (2026). A. Grebennikov and M. A. Kwan, “No‐(k+1)‐in‐line problem for large constant k,” <i>Bulletin of the London Mathematical Society</i>, vol. 58, no. 10. Wiley, 2026. Grebennikov, Aleksandr, and Matthew Alan Kwan. “No‐(K+1)‐in‐line Problem for Large Constant K.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2026. <a href="https://doi.org/10.1112/blms.70510">https://doi.org/10.1112/blms.70510</a>. 231232026-10-12T13:57:47Z2026-10-14T08:41:00Z