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 the same partition. For example, 4 can be partitioned
in five distinct ways:
4
3 + 1
2 + 2
2 + 1 + 1
1 + 1 + 1 + 1
The order-dependent composition 1 + 3 is the same partition
as 3 + 1, while the two distinct
compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same
partition 2 + 1 + 1.
Young diagrams associated to the partitions of the positive
integers 1 through 8. They are arranged so that images
under the reflection about the main diagonal of the square
are conjugate partitions.