Auxiliary functions for 'randtoolbox' package.
Stirling numbers of the second kind and permutation of positive integers.
stirling(n) permut(n)
n |
a positive integer. |
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 |
a vector with stirling numbers.
Christophe Dutang.
choose for combination numbers.
# should be 1 stirling(0) # should be 0,1,7,6,1 stirling(4)
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