This function computes Stirling numbers of the second kind, S(n, k), which count the number of ways of partitioning n distinct objects in to k non-empty sets.
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n |
A vector of one or more positive integers |
k |
A vector of one or more positive integers |
The implementation on this function is a simple recurrence relation which defines
S(n, k) = kS(n - 1, k), + S(n - 1, k - 1)
for k > 0 with the inital conditions S(0, 0) = 1 and S(n, 0) = S(0, n) = 0. If n
and n
have different lengths then expand.grid
is used to construct a vector of (n, k) pairs
An vector of Stirling numbers of the second kind
James Curran
http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind#Recurrence_relation
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