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arXiv · 1909.07762

Uniform asymptotic formulas of restricted bipartite partitions

Nian Hong Zhou
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Abstract

In this paper, we investigate $π(m,n)$, the number of partitions of the \emph{bipartite number} $(m,n)$ into \emph{steadily decreasing} parts, introduced by L.Carlitz ['A problem in partitions', Duke Math Journal 30 (1963), 203--213]. We give a relation between $π(m,n)$ and the crank statistic $M(m,n)$ for integer partitions. Using this relation, some uniform asymptotic formulas for $π(m,n)$ are established.

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Nian Hong Zhou. 2020-02-09. Uniform asymptotic formulas of restricted bipartite partitions. https://doi.org/10.1017/s0004972720000064

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