
Chapter 3
Stirling and Bell Numbers
In this chapter we recall the definition and basic properties of the classical Stirling and
Bell numbers. Many of these properties were already discussed in preceding chapters. For
instance, the Stirling numbers of the second kind, S(n, k), were introduced as the numbers
counting set partitions of the set [n] having k blocks, and later considerations showed that
they appear as connection coefficients when writing x
n
in terms of (x)
k
; see (1.3). We recall
that the numbers S(n, k) also appear as normal ordering coefficients for (XD)
n
and as rook
numbers of particular Ferrers boards. For the Bell numbers, which are closely ...