Partition theory, a central branch of combinatorial number theory, concerns itself with the enumeration and properties of the ways in which integers may be decomposed into sums of positive integers ...

A partition π of the set [n] = {1,2,..., n} is a collection {B₁...,Bk) of nonempty disjoint subsets of [n] (called blocks) whose union equals [n]. Suppose that the subsets Bi are listed in increasing ...