A correspondence between partitions related to generalizations of the Rogers-Ramanujan identities

Abstract

A 1-??? correspondence is established between partitions of a positive integer n of the form (p1p2p3...pn) where p1-pj+k-1≥2 and at most i-1 of the pj and partitions of n whose book differences dj all lie in the range -(i-2)≤2k-i-1. The same correspondence is also applied to partitions whose book differences lie in the range -(i-2)≤djk≤2k-i-2, and leads to further restrictions on the first set, and in particular to a correspondence between the partitions of a number n into distinct partsand the partitions of n whose book differences are all 0,1 or 2. © 1981.