Here and throughout this paper 191 is strictly less than one. Two new proofs of these identities have recently been announced. The first, by Lepowsky and Wilson [7], uses a Lie algebraic interpretation of the identities. The second, by Garsia and Milne (41, relies on the combinatorial interpretation and establishes the correspondence between the partitions which are counted by each side. Both of these proofs are enlightening but difficult. What is being presented here is the one type of proof… CONTINUE READING