A family of partitions with attached parts and ‘N copies of N’ Original Research Article

In this paper we find two distinct combinatorial interpretations for a family of summations with several free parameters. In one case we used partitions with attached parts and in the other partitions with ‘N copies of N’. There are interesting special cases including a description for a new set of partitions with the same cardinality of the one whose parts are congruent to j (mod k).