On the Ramsey number of the Brauer configuration
Combinatorics
2020-01-06 v2 Number Theory
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 nonlinear quadratic equations.
Keywords
Cite
@article{arxiv.1904.07567,
title = {On the Ramsey number of the Brauer configuration},
author = {Jonathan Chapman and Sean Prendiville},
journal= {arXiv preprint arXiv:1904.07567},
year = {2020}
}