PARTITION of a positive integer n

In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered to be the same partition; if order matters then the sum becomes a composition. For example, 4 can be partitioned in five distinct ways:

4,     3 + 1,     2 + 2,     2 + 1 + 1,     1 + 1 + 1 + 1.