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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 for symmetric polynomials, the symmetric group, and group representation.

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