Use this tag for questions related to ways of writing a positive integer as a sum of positive integers.
In number theory and combinatorics, a partition of a positive integer $n$ is a way of writing $n$ as a sum of positive integers. Two sums that differ only in the order of their summands (also called parts) are considered the same partition. For example, all of the partitions of 4 are 1 + 1 + 1 + 1, 2 + 1 + 1, 2 + 2, 3 + 1, or 4.
The number of partitions of $n$ is given by the partition function $p(n)$. For the example above, p(4) = 5.
Partitions can be visualized graphically with Ferrers diagrams.