Slinkies and the S-function content of certain generating functions

Abstract

A variety of methods are described for expanding particular generating functions in terms of their S-function content. Plethysms are used to establish conjugacy relations between S-function series and the task of evaluating certain products of classical S-function series introduced by Littlewood (1950) is then completed. Slinky diagrams are introduced to represent non-standard S-functions and their modification to give standard S-functions. The role of slinkies in determining the S-function content of other generating functions is then explained and exemplified.