A PASCAL-TYPE TRIANGLE FOR THE NUMBER OF TOPOLOGICALLY DISTINCT MANY-ELECTRON FEYNMAN GRAPHS

By expressing the Green function for a many-body system in terms of a perturbative expansion written as a sum over all connected and topologically distinct Feynman graphs, it is shown that the number of such diagrams can be iteratively obtained from a Pascal-type triangle. The key to the problem is to notice that it is possible to define on the set of graphs an equivalence relation, and that, from a well-known theorem of set theory, an equivalence relation on a set partitions it into disjoint classes.