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.

Partitions have applications in symmetric polynomials, the symmetric group, and group representations.