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