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In number theory and combinatorics, a partition of a non-negative 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. (If order matters, the sum becomes a composition.) For example, 4 can be partitioned in five distinct ways:
4
3 + 1
2 + 2
2 + 1 + 1
1 + 1 + 1 + 1
The only partition of zero is the empty sum, having no parts.
The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent...
In the number theory of integer partitions, the numbers
p
k
(
n
)
{\displaystyle p_{k}(n)}
denote both the number of partitions of
n
{\displaystyle n}
into exactly
k
{\displaystyle k}
parts (that is, sums of
k
{\displaystyle k}
positive integers that add to
n
{\displaystyle n}
), and the number of partitions...
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