Some New Congruences for Andrews' Singular Over partitions and 9-Regular Over partitions

Abstract

In this paper, we establish several new congruence relations for Andrews' singular overpartitions and -regular overpartitions. Specifically, we prove infinite families of congruences modulo 8 and 9 for, complementing earlier work on these partition functions. Additionally, we establish new congruences modulo 16 for extending recent results by Barman and Ray. Our proofs utilize Ramanujan's theta functions, cubic theta functions, and dissection formulas involving q-series identities. These results contribute to the growing body of arithmetic properties of singular and regular overpartition functions [1].