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  • 1904.07567

    Rights statement: This is the peer reviewed version of the following article: Chapman, J. and Prendiville, S. (2020), On the Ramsey number of the Brauer configuration. Bulletin of the London Mathematical Society, 52: 316-334. doi:10.1112/blms.12327 which has been published in final form at https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/blms.12327 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.

    Accepted author manuscript, 268 KB, PDF document

    Embargo ends: 14/04/21

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

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On the Ramsey number of the Brauer configuration

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/04/2020
<mark>Journal</mark>Bulletin of the London Mathematical Society
Issue number2
Volume52
Number of pages19
Pages (from-to)316-334
Publication statusPublished
Original languageEnglish

Abstract

We obtain a double exponential bound in Brauer's generalisation of van der Waerden's theorem, which concerns progressions with the same colour as their common difference. Such a result has been obtained independently and in much greater generality by Sanders. Using Gowers' local inverse theorem, our bound is quintuple exponential in the length of the progression. We refine this bound in the colour aspect for three‐term progressions, and combine our arguments with an insight of Lefmann to obtain analogous bounds for the Ramsey numbers of certain non‐linear quadratic equations.

Bibliographic note

This is the peer reviewed version of the following article: Chapman, J. and Prendiville, S. (2020), On the Ramsey number of the Brauer configuration. Bulletin of the London Mathematical Society, 52: 316-334. doi:10.1112/blms.12327 which has been published in final form at https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/blms.12327 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.