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.
Ramsey theory is sometimes characterized as the study of which collections
are partition regular.
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
are partition regular.
Much progress has been made recently on classifying nonlinear Diophantine equations.