On pairs of partitions with steadily decreasing parts

摘要

A new generating function identity for special pairs of partitions with steadily decreasing parts is proved via a bijection. Viewing such pairs of partitions (or, more generally, special r-tuples of partitions) as coloured modular Young diagrams also allows to give bijective proofs for generating function identities due to Carlitz and Andrews. (C) 2002 Elsevier Science (USA). [References: 4]