Integer partitions with even parts below odd parts and the mock theta functions (Q1787955)

In this interesting paper, the author investigates a couple of classes of partitions in which each even part is smaller than each odd part and remarks surprising connections with the even-odd crank (which is defined to be the largest even part minus the number of odd parts) and the third order mock theta function \[\nu(q) = \sum_{n=0}^\infty \frac{q^{n^2+n}}{(-q;q^2)_{n+1}}.\]