Linear relations for the number of overpartitions into odd parts

Abstract

Let $\overline{p}_o(n)$ denote the number of overpartitions of $n$ into odd parts. The partition function $\overline{p}_o(n)$ has been the subject of many recent studies where many explicit Ramanujan-like congruences were discovered. In this paper, we provide three linear recurrence relation for $\overline{p}_o(n)$. Several connections with partitions into parts not congruent to $2 \pmod 4$, overpartitions and partitions into distinct parts are presented in this context.

Theorems & Definitions (32)

• Theorem 1.1
• Theorem 1.2
• Theorem 1.3
• Theorem 1.4
• Theorem 1.5
• proof : Proof of Theorem \ref{['T1']}
• proof : Proof of Theorem \ref{['T2']}
• proof : Proof of Theorem \ref{['T3']}
• Theorem 3.1
• proof