The ACO Seminar (2013–2014)

A system of linear equations with integer coefficients is partition regular if, whenever the natural numbers are finitely coloured, it has a monochromatic solution. Rado gave a good characterisation of the finite partition regular systems, but even examples of infinite partition regular systems are hard to find.

I will describe a new family of infinite partition regular systems, and how it can be used to answer a long-standing open question: if a system of equations is partition regular over the rationals, must it also be partition regular over the natural numbers?

Joint work with Neil Hindman and Imre Leader.