Partitions of large unbalanced bipartites

We compute the asymptotic behaviour of the number of partitions of large vectors $(n_1,n_2)$ of ${\mathbb{Z}}_{+}^2$ in the critical regime $n_1 \asymp \sqrt{n_2}$andinthesubcriticalregime$n_1 = o(\sqrt{n_2})$. This work completes the results established in the fifties by Auluck, Nanda, and Wright.