Internal congruences modulo powers of $2$ for overpartition tuples with odd parts

Manjil P. Saikia, Prabal Talukdar

Let ${\overline{\mathrm{OPT}}}_m(n)$ denote the number of overpartition $m$-tuples of $n$ into odd parts. We prove that for every odd $m\ge 1$ and every $i\ge 3$, \[\sum_{n\ge0}\Bigl(\…