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Thursday, December 15, 2011

Stirling numbers of the first kind.

Definition. S1[n,k] (Stirling number of the first kind) is the number of permutations of length n containing k cycles, multiplied by the sign of these permutations.

Example: 
Permutation     Cycles
123             (1)(2)(3)
132             (1)(23)
213             (12)(3)
231             (123)
312             (132)
321             (13)(2)
Thus:
S1[3,1]=2
S1[3,2]=-3
S1[3,3]=1

Stirling Numbers of the first kind are implemented in Mathematica as StirlingS1.
Posted by at 5:32:00 PM
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