On the Ramsey number of the Brauer configuration

Prendiville, Sean and Chapman, Jonathan (2020) On the Ramsey number of the Brauer configuration. Bulletin of the London Mathematical Society, 52 (2). pp. 316-334. ISSN 0024-6093

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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.

Item Type:
Journal Article
Journal or Publication Title:
Bulletin of the London Mathematical Society
Additional Information:
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.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
140244
Deposited By:
Deposited On:
16 Jan 2020 16:35
Refereed?:
Yes
Published?:
Published
Last Modified:
06 Jul 2020 01:45