3 papers
math.NT2020
Partition regularity for systems of diagonal equations
Jonathan Chapman
We consider systems of diagonal equations in th powers. Our main result shows that if the coefficient matrix of such a system is sufficiently non-singular, then the system i…
math.CO2019
On the Ramsey number of the Brauer configuration
Jonathan Chapman, Sean Prendiville
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 re…
math.CO2019
Partition regularity and multiplicatively syndetic sets
Jonathan Chapman
We show how multiplicatively syndetic sets can be used in the study of partition regularity of dilation invariant systems of polynomial equations. In particular, we prove that a di…