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On the Ramsey number of the Brauer configuration
Author(s) -
Chapman Jonathan,
Prendiville Sean
Publication year - 2020
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12327
Subject(s) - van der waerden's theorem , mathematics , generality , exponential function , upper and lower bounds , quadratic equation , inverse , combinatorics , pure mathematics , discrete mathematics , mathematical analysis , geometry , psychology , psychotherapist
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.