[{"mathsc":["05D40","52C10","52C35"],"year":"2026","title":"No‐(k+1)‐in‐line problem for large constant k","date_updated":"2026-10-14T08:41:00Z","doi":"10.1112/blms.70510","status":"public","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","PlanS_conform":"1","_id":"23123","intvolume":"        58","publisher":"Wiley","author":[{"last_name":"Grebennikov","full_name":"Grebennikov, Aleksandr","first_name":"Aleksandr","id":"776468ec-50b0-11ef-861e-96ad19e894f3"},{"full_name":"Kwan, Matthew Alan","last_name":"Kwan","orcid":"0000-0002-4003-7567","first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"}],"oa":1,"corr_author":"1","das_tickbox":"0","fulldoi":"https://doi.org/10.1112/blms.70510","date_published":"2026-10-01T00:00:00Z","type":"journal_article","date_created":"2026-10-12T13:57:47Z","article_number":"e70510","month":"10","OA_place":"publisher","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"MaKw"},{"_id":"GradSch"}],"OA_type":"hybrid","publication_status":"published","abstract":[{"lang":"eng","text":"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"}],"volume":58,"supplementarymaterial":"no","scopus_import":"1","day":"01","article_type":"original","researchdata_availability":"no","project":[{"name":"Randomness and structure in combinatorics","grant_number":"101076777","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"ddc":["510"],"publication":"Bulletin of the London Mathematical Society","license":"https://creativecommons.org/licenses/by/4.0/","language":[{"iso":"eng"}],"acknowledgement":"We would like to thank Huy Pham for insightful discussions about the proof approach, and wewould like to thank the anonymous referees for their careful reading and helpful comments. Bothauthors are supported by ERC Starting Grant “RANDSTRUCT” No. 101076777.Open Access funding provided by Institute of Science and Technology Austria.","issue":"10","oa_version":"Published Version","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"citation":{"apa":"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>","short":"A. Grebennikov, M.A. Kwan, Bulletin of the London Mathematical Society 58 (2026).","chicago":"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>.","ieee":"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.","ama":"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>","ista":"Grebennikov A, Kwan MA. 2026. No‐(k+1)‐in‐line problem for large constant k. Bulletin of the London Mathematical Society. 58(10), e70510.","mla":"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>."},"publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"file":[{"content_type":"application/pdf","checksum":"cce830e3fc66174803b91103f5b88a29","file_name":"2026_BulletinLondonMathSoc_Grebennikov.pdf","date_created":"2026-10-14T08:37:16Z","relation":"main_file","file_id":"23139","file_size":284851,"creator":"dernst","success":1,"access_level":"open_access","date_updated":"2026-10-14T08:37:16Z"}],"file_date_updated":"2026-10-14T08:37:16Z"}]