New Combinatorial Interpretations for the Partitions into Odd Parts Greater than One

Abstract

In this paper, we consider $Q_1(n)$ to be the number of partitions of $n$ into odd parts greater than one and provide new combinatorial interpretations for $Q_1(n)$. New linear relations involving Euler's partition function $p(n)$ and the overpartition function $\overline{p}(n)$ are obtained in this context.