Extensive parity analysis of broken 5-diamond partitions

Abstract

In this paper, we investigate congruences for [Formula: see text] modulo 2 and characterize the parity of [Formula: see text] and [Formula: see text] according to the arithmetic property of [Formula: see text]. As a consequence, we obtain various Ramanujan type congruences for [Formula: see text]. We also extend these results to several infinite families of congruences.