Stirling Numbers of the Second Kind
The Stirling numbers of the second kind, or Stirling partition numbers, sometimes denoted , count the number of ways to partition a set of elements into discrete, nonempty subsets. This Demonstration illustrates the different partitions that a Stirling partition number counts. The sums of the Stirling partition numbers are the Bell numbers.
Snapshot 1: there is only one way to partition elements into nonempty subsets, and therefore
Snapshot 2: similarly, there is only one way to partition elements into 1 nonempty subset, which means that
Snapshot 3: the Stirling numbers of the second kind can be computed recursively; by comparing Snapshot 2 and Snapshot 3, it is apparent that and are related