On 3- and 9-regular overpartitions modulo powers of 3
Volume 154 / 2018
Colloquium Mathematicum 154 (2018), 121-130
MSC: Primary 11P83.
DOI: 10.4064/cm7317-10-2017
Published online: 6 August 2018
Abstract
Let $\overline { A}_3(n)$ and $\overline { A}_9(n)$ denote the number of 3- and 9-regular overpartitions of $n$. For each $\alpha \gt 0$, we obtain the generating functions for $\overline { A}_{3}(3^{2\alpha }n )$, $\overline { A}_{3}(3^{2\alpha -1}n )$ and $\overline { A}_{9} (3^{\alpha }n)$. We show that $\overline { A}_{3}(n)$ and $\overline { A}_{9}(n)$ satisfy certain internal congruences.
