
38 Commutation Relations, Normal Ordering, and Stirling Numbers
Definition 2.47 A partition λ = λ
1
λ
2
···λ
k
is a weakly decreasing sequence of positive
integers which are called parts. We denote the sum of the parts of λ by |λ|, that is, |λ| =
k
i=1
λ
i
.If|λ| = n,thenλ is said to be a partition of n, denoted by λ n.
Example 2.48 There is only one partition of 1,namely1. There are two partitions of 2
(11 and 2) and three partitions of 3(111, 21 and 3).
The generating function for the number of partitions of n has received a lot of attention,
for example, see [33].
Theorem 2.49 The generating function for the number of partitions of n is given by
n≥0
λ