Products of class operators of the symmetric group

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AbstractA combinatorial derivation of the product of the class of three cycles, [(1)N−3(3)]N with an arbitrary class operator of the symmetric group SN is presented. The form of this result suggests a conjecture concerning the expression of the general class operator product in terms of a relatively small number of reduced class coefficients. The conjecture is applied to the determination of the products of [(1)N−4(4)]N, [(1)N−4(2)2]N, and [(1)N−5(5)]N with arbitrary class operators. General expressions for the reduced class coefficients of the simplest type are obtained.