auxiliary {randtoolbox}

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)