cycle index polynomial

The cycle index polynomial of given permutation group counts the number of group elements of a given cycle type. In Symmetrica there routines to do this computation for different finite groups. There are routines to compute the cycle index polynomial for the following permutation groups:

redball symmetric group [try]
redball alternating group [try]
redball cyclic group [try]
redball dihedral group [try]
redball permutation group given by generators [try]

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