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Stirling Numbers of the Second Kind

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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

Snapshots

Details

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

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