randtoolbox (version 2.0.2)

auxiliary: Auxiliary functions for 'randtoolbox' package.

Description

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

Usage

stirling(n)
permut(n)

Value

a vector with stirling numbers.

Arguments

n

a positive integer.

Author

Christophe Dutang.

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

See Also

choose for combination numbers.

Examples

# should be 1
stirling(0)

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