---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '23123'
abstract:
- lang: eng
  text: "How many points can be placed in an \U0001D45B × \U0001D45B grid sothat every
    (affine) line contains at most \U0001D458 points? Weprove that for \U0001D45B
    ⩾ \U0001D458 ⩾ 1037 the maximum number ofpoints is exactly \U0001D458\U0001D45B.
    Our proof builds on the recent workof Kovács, Nagy and Szabó (who proved an analogousresult
    when \U0001D458 is at least about √\U0001D45B log \U0001D45B), incorporat-ing
    ideas of Jain and Pham. Using the same approach,we also obtain new bounds for
    higher-dimensionalextensions of this problem"
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.
article_number: e70510
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Aleksandr
  full_name: Grebennikov, Aleksandr
  id: 776468ec-50b0-11ef-861e-96ad19e894f3
  last_name: Grebennikov
- first_name: Matthew Alan
  full_name: Kwan, Matthew Alan
  id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
  last_name: Kwan
  orcid: 0000-0002-4003-7567
citation:
  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>
  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>
  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.
  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>.
  short: A. Grebennikov, M.A. Kwan, Bulletin of the London Mathematical Society 58
    (2026).
corr_author: '1'
das_tickbox: '0'
date_created: 2026-10-12T13:57:47Z
date_published: 2026-10-01T00:00:00Z
date_updated: 2026-10-14T08:41:00Z
day: '01'
ddc:
- '510'
department:
- _id: MaKw
- _id: GradSch
doi: 10.1112/blms.70510
file:
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  date_created: 2026-10-14T08:37:16Z
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fulldoi: https://doi.org/10.1112/blms.70510
has_accepted_license: '1'
intvolume: '        58'
issue: '10'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
mathsc:
- 05D40
- 52C10
- 52C35
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: bd95085b-d553-11ed-ba76-e55d3349be45
  grant_number: '101076777'
  name: Randomness and structure in combinatorics
publication: Bulletin of the London Mathematical Society
publication_identifier:
  eissn:
  - 1469-2120
  issn:
  - 0024-6093
publication_status: published
publisher: Wiley
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: No‐(k+1)‐in‐line problem for large constant k
tmp:
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  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2026'
...