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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.

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.

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.

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.

Questions related to the different ways of expressing an integer as a sum of integers; or, questions related to the subdivision of the edge or vertex set of a (hyper)graph.

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.