Partitions of large unbalanced bipartites

Abstract

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 $n_1\asymp \sqrt{n_2}$ and in the subcritical regime $n_1=o(\sqrt{n_2})$. This work completes the results established in the fifties by Auluck, Nanda, and Wright.

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• $\mathcal{N}=2^{\ast }$ Schur indices