Abstract: | An algorithm for the evaluation of the structure constants in the class algebra of the symmetric group has recently been considered. The product of the class sum [(p)]n that consists of a cycle of length p and n−p fixed points, with an arbitrary class sum in Sn, was found to be expressible in terms of a set of reduced class coefficients (RCCs), the p-RCCs. The combinatorial significance of the p-RCCs is elucidated, showing that they are related to a well-defined enumeration problem within Sp, which has to do with a certain refinement of the corresponding class multiplication problem. This is in contrast with the representation-theoretic evaluation of the p-RCCs, which requires the evaluation of products involving [(p)]n for several values of n > p. The combinatorial interpretation of the p-RCCs allows the derivation of some of their previously conjectured properties and of some of the “elimination rules” that specific types of p-RCCs were found to satisfy. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 103–118, 1998 |