CycleIndexPolynomial

CycleIndexPolynomial[perm, {x1, ..., xn}] constructs the cycle index monomial of the permutation perm in the variables xi.

CycleIndexPolynomial[group, {x1, ..., xn}] constructs the cycle index polynomial of group in the variables xi.

Examples

Cycle index of a permutation:

CycleIndexPolynomial[Cycles[{{1, 2, 3}}], {x1, x2, x3}]
(* x3 *)

For a symmetric group:

CycleIndexPolynomial[SymmetricGroup[3], {x1, x2, x3}]

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