Wolfram Demonstrations Project

13,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Stirling Numbers of the Second Kind

Initializing live version
Download to Desktop

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

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

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send