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.
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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - On the Ramsey number of the Brauer configuration
AU - Prendiville, Sean
AU - Chapman, Jonathan
N1 - 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.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - 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.
AB - 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.
U2 - 10.1112/blms.12327
DO - 10.1112/blms.12327
M3 - Journal article
VL - 52
SP - 316
EP - 334
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
SN - 0024-6093
IS - 2
ER -