Extending Theorems of Göllnitz,A New Family of Partition Identities

A new family of partition identities is given which include as special cases two theorems of Göllnitz. We show, also, a relation between our result and a theorem given by Sylvester.     

A Family of Partition Identities Proved Combinatorially

We present three infinite families of partitions that, for corresponding parameters, are equinumerous. This generalizes an identity proved by the first author (Pacific Journal of Mathematics, 77(1) (1978)) and two identities proved by the second and third authors (Relatório Técnico 08/99 IMECC-UNICAMP, 1999).