EXTENDING CONGRUENCES FOR OVERPARTITIONS WITH $\ell $-REGULAR NONOVERLINED PARTS

Abstract 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.