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.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

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
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.