Stirling number of the second kind

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The number S(n, r) of ways of partitioning a set of n elements into r non-empty subsets. For example, the set {1, 2, 3, 4} can be partitioned into two non-empty subsets in the following ways:So S(4, 2)=7. Clearly, S(n, 1)=1 and S(n, n)=1. It can be shown that

S(n+1, r)=S(n, r−1)+rS(n, r)

Rather like the binomial coefficients, the Stirling numbers occur as coefficients in certain identities. They are named after the Scottish mathematician James Stirling (1692–1770).

Subjects: Mathematics.

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