Partitions of large unbalanced bipartites

Julien Bureaux (1)

1 MODAL'X - Modélisation aléatoire de Paris X

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.

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]

Julien Bureaux. Partitions of large unbalanced bipartites. 2014. ⟨hal-00940147v2⟩