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ON THE DISTRIBUTION OF THE RANK STATISTIC FOR STRONGLY CONCAVE COMPOSITIONS

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  13 February 2019

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, Shanghai 200241, PR China email [email protected]
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Abstract

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A strongly concave composition of $n$ is an integer partition with strictly decreasing and then increasing parts. In this paper we give a uniform asymptotic formula for the rank statistic of a strongly concave composition introduced by Andrews et al. [‘Modularity of the concave composition generating function’, Algebra Number Theory7(9) (2013), 2103–2139].

Keywords

concave compositionpartitionsrankasymptotics

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 100 , Issue 2 , October 2019 , pp. 230 - 238
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

This research was supported by the National Science Foundation of China (Grant No. 11571114).

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