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 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.
