Counting Partitions
The total number of partitions of an n-element set is the Bell number Bn. The first several Bell numbers are B0 = 1, B1 = 1, B2 = 2, B3 = 5, B4 = 15, B5 = 52, and B6 = 203. Bell numbers satisfy the recursion
and have the exponential generating function
The number of partitions of an n-element set into exactly k nonempty parts is the Stirling number of the second kind S(n, k).
The number of noncrossing partitions of an n-element set is the Catalan number Cn, given by
Read more about this topic: Partition Of A Set
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