A Bijection Between Two Different Classes of Partitions Enumerated by $p_{\nu }(n)$

Abstract

In this paper, we give a purely bijective proof that two different partition classes that are both combinatorial interpretations of the partition function $p_{\nu }(n)$, a partition function related to the third order mock theta function $\nu (q)$, are equinumerous. In doing so, we give a partial solution to a combinatorial problem proposed in a paper by Andrews.