MultipartitionIn number theory and combinatorics, a multipartition of a positive integer n is a way of writing n as a sum, each element of which is in turn an integer partition. The concept is also found in the theory of Lie algebras.r-component multipartitionsAn r-component multipartition of an integer n is an r-tuple of partitions λ,..., λ where each λ is a partition of some ai and the ai sum to n. The number of r-component multipartitions of n is denoted Pr. Congruences for the function Pr have been studied by A. O. L. Atkin.