[For the entire collection see Zbl 0674.00006.]
This paper is an exposition and elaboration on the work of W. H. Burge which demonstrates the connection among various combinatorial interpretations of the multiple summations which arise in the generalizations of the Rogers-Ramanujan identities. Some new results on partitions with restrictions on successive ranks are presented and the Rogers-Ramanujan identities are extended to words in three letters weighted by the major index.
In section 1, the terminology of lattice paths is defined to present the interpretation of several multiple series identities. In section 2, proofs of the interpretations are indicated. In section 3, connection between weighted lattice paths and successive ranks are explored and in section 4, the connecton to frequency restrictions is presented. Section 5 consists of new results on analogs of the Rogers-Ramanujan identities in which words in three letters are weighted by their major indices.