R: Compute Stirling numbers of the second kind

Stirling2 {multicool} | R Documentation

## Compute Stirling numbers of the second kind

### 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

    Stirling2(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

    ## 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)

[Package multicool version 0.1-11 Index]