On the Ramsey number of the Brauer configuration

Jonathan Chapman, Sean Prendiville

Research output: Contribution to journalArticle (Academic Journal)peer-review

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.
Original languageEnglish
Pages (from-to)316-334
JournalBulletin of the London Mathematical Society
Volume52
DOIs
Publication statusPublished - 14 Apr 2020

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