Stirling Numbers of the Second Kind
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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.
Contributed by: Robert Dickau (March 2011)
Open content licensed under CC BY-NC-SA
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