Stirling numbers of the second kind

Numbers parameterizing ways to partition a set

In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by S ( n , k) {\displaystyle S(n,k)} or { n k } {\displaystyle \textstyle \left\{{n \atop k}\right\}} . Stirling numbers of the second kind occur in combinatorics and the study of partitions. They are named after James Stirling.

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