R: Auxiliary functions for 'randtoolbox' package.

auxiliary {randtoolbox} | R Documentation

## Auxiliary functions for 'randtoolbox' package.

### Description

Stirling numbers of the second kind and permutation of positive integers.

### Usage

    stirling(n)
    permut(n)

### Arguments

`n` | a positive integer.

### Details

`stirling` computes stirling numbers of second kind i.e.

Stirl_n^k = k * Stirl_{n-1}^k + Stirl_{n-1}^{k-1}

with Stirl_n^1 = Stirl_n^n = 1. e.g.

- n = 0, returns 1

- n = 1, returns a vector with 0,1

- n = 2, returns a vector with 0,1,1

- n = 3, returns a vector with 0,1,3,1

- n = 4, returns a vector with 0,1,7,6,1...

Go to wikipedia for more details.

`permut` compute permutation of {1, ..., n} and store it in a matrix. e.g.

- n=1, returns a matrix with

  1

- n=2, returns a matrix with

  1 | 2
  2 | 1

- n=3 returns a matrix with

  3 | 1 | 2
  3 | 2 | 1
  1 | 3 | 2
  2 | 3 | 1
  1 | 2 | 3
  2 | 1 | 3

### Value

a vector with stirling numbers.

### Author(s)

Christophe Dutang.

### See Also

`choose` for combination numbers.

### Examples

    # should be 1
    stirling(0)

    #  should be 0,1,7,6,1
    stirling(4)

[Package randtoolbox version 2.0.1 Index]