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UNIFORM ASYMPTOTIC FORMULAS FOR RESTRICTED BIPARTITE PARTITIONS

Part of: Combinatorics Additive number theory; partitions

Published online by Cambridge University Press:  05 February 2020

NIAN HONG ZHOU Open the ORCID record for NIAN HONG ZHOU [Opens in a new window]
NIAN HONG ZHOU*
Affiliation:
School of Mathematical Sciences, East China Normal University, Shanghai200241, PR China email nianhongzhou@outlook.com
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Abstract

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 $\unicode[STIX]{x1D70B}(m,n)$.

Keywords

partitionsrestricted partitionsasymptotics

MSC classification

Primary: 11P82: Analytic theory of partitions
Secondary: 05A16: Asymptotic enumeration 05A17: Partitions of integers
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 2 , October 2020 , pp. 217 - 225
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This research was supported by the National Science Foundation of China (Grant No. 11971173).

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