New Ramanujan-like congruences modulo powers of 2 and 3 for overpartitions
Let \(\overline{p}(n)\) denote the number of overpartitions of \(n\). There are five theorems in the paper, containing \(13\) congruences. The following are typical examples: \[ \begin{aligned} \overline{p}(24n+19) &\equiv 0 \pmod{27}, \\ \overline{p}(72n+69) &\equiv 0 \pmod{32}, \\ \overline{p}(48n+2) &\equiv \begin{cases} 4 \pmod{8}, &\text{if \(n = k(3k \pm 1)/2\)}, \\ 0 \pmod{8}, &\text{otherwise}. \end{cases} \end{aligned} \] The proofs are elementary, beginning with known infinite product generating functions for \(\overline{p}(3n+x)\), \(0 \leq x \leq 2\), and then applying a variety of \(2\)-dissections.
scientific article; zbMATH DE number 6154099