In combinatorics, a branch of mathematics, partition regularity is one notion of largeness for a collection of sets.
is called partition regular if every set A in the collection has the property that, no matter how A is partitioned into finitely many subsets, at least one of the subsets will also belong to the collection.
, and any finite partition
Ramsey theory is sometimes characterized as the study of which collections
A Diophantine equation
is called partition regular if the collection of all infinite subsets of
containing a solution is partition regular.
Rado's theorem characterises exactly which systems of linear Diophantine equations
Much progress has been made recently on classifying nonlinear Diophantine equations.