CLASS-SUM PRODUCTS IN THE SYMMETRICAL GROUP - MINIMALLY-CONNECTED REDUCED CLASS COEFFICIENTS

The class algebra of the symmetric group plays an important role in th e study of systems of identical particles. Recent progress in an ongoi ng effort to develop an algorithm for the combinatorial evaluation of the corresponding structure constants is presented. A connection is es tablished with a closed form expression for a certain set of structure constants, obtained by Goupil and Bedard, and by Goulden and Jackson. This allows the evaluation of a corresponding set of reduced coeffici ents that, in turn, have considerably wider applicability. Some outsta nding open problems are presented.