Binomial transforms and integer partitions into parts of k different magnitudes

A relationship between the general linear group of degree n over a finite field and the integer partitions of n into parts of k different magnitudes was investigated recently by the author. In this paper, we use a variation of the classical binomial transform to derive a new connection between partitions into parts of k different magnitudes and another finite classical group, namely the symplectic group Sp. New identities involving the number of partitions of n into parts of k different magnitudes are introduced in this context.