THE ENUMERATIVE USES OF GENERATING FUNCTIONS.
Edward A. Bender, Jay R. Goldman · 1969
Abstract : 'Objects' may be viewed as a product of 'prime objects' in such a way that the appropriate type of generating function is immediately suggested by the combinatorial problem. Many graph theory formulae (rooted trees, chromatic labeled graphs, etc) follow easily. Other immediate consequences are e to the power((e to the power x)-1) for partitions of a set, and the enumeration of direct sum decompositions of finite vector spaces. (Author)