Stirling2: Compute Stirling numbers of the second kind

Description Usage Arguments Details Value Author(s) References Examples

Description

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.

Usage

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Stirling2(n, k)
S2(n, k)

Arguments

n

A vector of one or more positive integers

k

A vector of one or more positive integers

Details

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

Value

An vector of Stirling numbers of the second kind

Author(s)

James Curran

References

http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind#Recurrence_relation

Examples

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## returns S(6, 3)
Stirling2(6, 3)

## returns S(6,1), S(6,2), ..., S(6,6)
S2(6, 1:6)

## returns S(6,1), S(5, 2), S(4, 3)
S2(6:4, 1:3)


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