Journal article
New lower bounds for van der Waerden numbers
- Abstract:
- We show that there is a red-blue colouring of [N] with no blue 3-term arithmetic progression and no red arithmetic progression of length eC(logN)3/4(loglogN)1/4. Consequently, the two-colour van der Waerden number w(3,k) is bounded below by kb(k), where b(k)=c(logkloglogk)1/3. Previously it had been speculated, supported by data, that w(3,k)=O(k2).
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Version of record, pdf, 799.8KB, Terms of use)
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- Publisher copy:
- 10.1017/fmp.2022.12
Authors
- Publisher:
- Cambridge University Press
- Journal:
- Forum of Mathematics, Pi More from this journal
- Volume:
- 10
- Article number:
- e18
- Publication date:
- 2022-07-13
- Acceptance date:
- 2022-03-08
- DOI:
- EISSN:
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2050-5086
- Language:
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English
- Keywords:
- Pubs id:
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1269507
- Local pid:
-
pubs:1269507
- Deposit date:
-
2022-10-10
Terms of use
- Copyright holder:
- Ben Green
- Copyright date:
- 2022
- Rights statement:
- © The Author(s), 2022. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Licence:
- CC Attribution (CC BY)
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