Lattice paths and the Rogers-Ramanujan identities

Abstract

This is an exposition and elaboration on work of W.H. Burge which demonstrates the connections among the various combinatorial interpretations of the multiple summations which arise in generalizations of the Rogers-Ramanujan identities. It includes some new results on partitions with restrictions on the succesive ranks and an extension of the Rogers-Ramanujan identities to words in three letters weighted by the major index.