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

TL;DR

This paper provides a bijective proof demonstrating the equinumerosity of two partition classes related to the third order mock theta function, addressing a combinatorial problem posed by Andrews.

Contribution

It introduces a bijective proof linking two classes of partitions associated with the function p_ν(n), offering a partial solution to a problem by Andrews.

Findings

Two classes of partitions are shown to be equinumerous via bijection.

The proof relates to the third order mock theta function ν(q).

Addresses a combinatorial problem proposed by Andrews.

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.