The ACO Seminar (2013–2014)
, 3:30pm, Wean 8220
, University of Cambridge
Partition regularity in the rationals
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.
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