New congruences modulo powers of 2 for k-regular overpartition pairs

Abstract

Let $\overline{B}_{k}(n)$ denote the number of $k$ regular overpartition pairs where a $k$-regular overpartition pair of $n$ is a pair of $k$-regular overpartitions $(a,b)$ in which the sum of all the parts is $n$. Naika and Shivasankar (2017) proved infinite families of congruences for $\overline{B}_3(n)$ and $\overline{B}_4(n)$. In this paper, we prove infinite families of congruences modulo powers of $2$ for $\overline{B}_{3\gamma}(n)$, $\overline{B}_{4\gamma}(n)$ and $\overline{B}_{6\gamma}(n)$.