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    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

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On the Ramsey number of the Brauer configuration

Research output: Contribution to journalJournal article

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On the Ramsey number of the Brauer configuration. / Prendiville, Sean; Chapman, Jonathan.

In: Bulletin of the London Mathematical Society, Vol. 52, No. 2, 01.04.2020, p. 316-334.

Research output: Contribution to journalJournal article

Harvard

Prendiville, S & Chapman, J 2020, 'On the Ramsey number of the Brauer configuration', Bulletin of the London Mathematical Society, vol. 52, no. 2, pp. 316-334. https://doi.org/10.1112/blms.12327

APA

Prendiville, S., & Chapman, J. (2020). On the Ramsey number of the Brauer configuration. Bulletin of the London Mathematical Society, 52(2), 316-334. https://doi.org/10.1112/blms.12327

Vancouver

Prendiville S, Chapman J. On the Ramsey number of the Brauer configuration. Bulletin of the London Mathematical Society. 2020 Apr 1;52(2):316-334. https://doi.org/10.1112/blms.12327

Author

Prendiville, Sean ; Chapman, Jonathan. / On the Ramsey number of the Brauer configuration. In: Bulletin of the London Mathematical Society. 2020 ; Vol. 52, No. 2. pp. 316-334.

Bibtex

@article{d56a1401c68b4f239cec2a35012e59c5,
title = "On the Ramsey number of the Brauer configuration",
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.",
author = "Sean Prendiville and Jonathan Chapman",
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. ",
year = "2020",
month = apr,
day = "1",
doi = "10.1112/blms.12327",
language = "English",
volume = "52",
pages = "316--334",
journal = "Bulletin of the London Mathematical Society",
issn = "0024-6093",
publisher = "Oxford University Press",
number = "2",

}

RIS

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 -