UNIFORM ASYMPTOTIC FORMULAS FOR RESTRICTED BIPARTITE PARTITIONS
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 cr...
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| Veröffentlicht in: | Bulletin of the Australian Mathematical Society 2020-10, Vol.102 (2), p.217-225 |
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| creator | ZHOU, NIAN HONG |
| description | 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 $\unicode[STIX]{x1D70B}(m,n)$. |
| doi_str_mv | 10.1017/S0004972720000064 |
| format | Article |
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| source | Cambridge University Press Journals Complete |
| subjects | Asymptotic properties |
| title | UNIFORM ASYMPTOTIC FORMULAS FOR RESTRICTED BIPARTITE PARTITIONS |
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