Last data update: 2014.03.03
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R: Auxiliary functions for 'randtoolbox' package.
Auxiliary functions for 'randtoolbox' package.
Description
Stirling numbers of the second kind and permutation of positive integers.
Usage
stirling(n)
permut(n)
Arguments
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
n=2, returns a matrix with
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)
Results
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