EXTENDING CONGRUENCES FOR OVERPARTITIONS WITH ℓ-REGULAR NONOVERLINED PARTS

Recently, Alanazi et al. ['Refining overpartitions by properties of nonoverlined parts', Contrib. Discrete Math. 17(2) (2022), 96-111] considered overpartitions wherein the nonoverlined parts must be & ell;-regular, that is, the nonoverlined parts cannot be divisible by the integer & ell;. In the process, they proved a general parity result for the corresponding enumerating functions. They also proved some specific congruences for the case & ell; = 3. In this paper we use elementary generating function manipulations to significantly extend this set of known congruences for these functions.