Congruences for some partition functions

Abstract

Recently, Andrews carried out a thorough investigation of integer partitions in which all parts of a given parity are smaller than those of the opposite parity. Further, considering a subset of this set of partitions, he obtains several interesting arithmetic and combinatorial properties and its connections to the third order mock theta function v(q). In this paper, we study certain congruences satisfied by the above set of partitions (and the subset above) along with a certain subset of partitions (of Andrews' partitions above) studied by Uncu. We also obtain certain family of congruences modulo 2 for the Ramanujan tau function. © 2022 Ramanujan Mathematical Society. All rights reserved.