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.


	Contributed by: Robert Dickau
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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

Stirling Number of the Second Kind (Wolfram MathWorld)

Small Set Partitions (The Wolfram Demonstrations Project)

Stirling's Triangles (The Wolfram Demonstrations Project)

"Stirling Numbers of the Second Kind" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/StirlingNumbersOfTheSecondKind/

Contributed by: Robert Dickau

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