The Stirling numbers of the second kind
describe the number of ways a set with *n* elements can be partitioned into
*k* disjoint, non-empty subsets.

For example, the set {1, 2, 3} can be partitioned into three subsets
in the following way --

into two subsets in the following ways --

and into one subset in the following way --

The numbers can be computed recursively using this formula:

Here are some diagrams representing the different ways the sets can be partitioned: a line connects elements in the same subset, and a point represents a singleton subset.

`StirlingS2[3, k]`

:

`StirlingS2[4, k]`

:

`StirlingS2[5, k]`

:

`StirlingS2[6, k]`

:

The sums of the Stirling numbers of the second kind,

are called the
*Bell numbers*.

Designed and rendered using *Mathematica* 3.0 for the Apple Macintosh.

Copyright © 1996 Robert M. Dickau