Multipartition
In 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 a partition. The concept is also found in the theory of Lie algebras. r-component multipartitions. An "r"-component multipartition of an integer "n" is an "r"-tuple of partitions λ...,λ where each λ is a partition of some "a" and the "a" sum to "n". The number of "r"-component multipartitions of "n" is denoted "P"("n"). Congruences for the function "P"("n") have been studied by A. O. L. Atkin.