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UNIFORM ASYMPTOTIC FORMULAS FOR RESTRICTED BIPARTITE PARTITIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 102 / Issue 2 / October 2020
- Published online by Cambridge University Press:
- 05 February 2020, pp. 217-225
- Print publication:
- October 2020
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- Article
- Export citation
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In this paper, we investigate
$\unicode[STIX]{x1D70B}(m,n)$, the number of partitions of the bipartite number
$(m,n)$ into steadily decreasing parts, introduced by Carlitz [‘A problem in partitions’, Duke Math. J.30 (1963), 203–213]. We give a relation between 
$\unicode[STIX]{x1D70B}(m,n)$ and the crank statistic 
$M(m,n)$ for integer partitions. Using this relation, we establish some uniform asymptotic formulas for 
$\unicode[STIX]{x1D70B}(m,n)$.
