auxfun: Auxiliary functions for 'randtoolbox' package.

In randtoolbox: Toolbox for Pseudo and Quasi Random Number Generation and Random Generator Tests

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 all permutations of {1, ..., n} and store it in a matrix of n columns. 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 or a matrix with permutations.

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)

randtoolbox documentation built on Oct. 18, 2024, 5:13 p.m.