Congruences Modulo Powers of 3 for 3- and 9-Colored Generalized Frobenius Partitions

Abstract

Let cφ k (n) be the number of k-colored generalized Frobenius partitions of n. We establish some infinite families of congruences for cφ3(n) and cφ9(n) modulo arbitrary powers of 3, which refine the results of Kolitsch. For example, for k ≥ 3 and n ≥ 0, we prove thatWe give two different proofs to the congruences satisfied by cφ9(n). One of the proofs uses an relation between cφ9(n) and cφ3(n) due to Kolitsch, for which we provide a new proof in this paper.