Auxiliary functions for 'randtoolbox' package.

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Description

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

Usage

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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

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5
# should be 1
stirling(0)

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