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INEQUALITIES AND UNIFORM ASYMPTOTIC FORMULAE FOR SPT-CRANK OF PARTITIONS

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  13 September 2024

YUAN CHEN  and
NIAN HONG ZHOU Open the ORCID record for NIAN HONG ZHOU [Opens in a new window]
YUAN CHEN
Affiliation:
School of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi, PR China e-mail: yuanchen0218@outlook.com
NIAN HONG ZHOU*
Affiliation:
School of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi, PR China
*
e-mail: nianhongzhou@outlook.com
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Abstract

We establish some inequalities that arise from truncating Lerch sums and derive uniform asymptotic formulae for the spt-crank of ordinary partitions. The uniform asymptotic formulae improve upon a result of Mao [‘Asymptotic formulas for spt-crank of partitions’, J. Math. Anal. Appl. 460(1) (2018), 121–139].

Keywords

integer partitionsspt-crankuniform asymptotics

MSC classification

Primary: 11P82: Analytic theory of partitions
Secondary: 05A16: Asymptotic enumeration 05A17: Partitions of integers

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 111 , Issue 1 , February 2025 , pp. 56 - 67
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Nian Hong Zhou was partially supported by the National Natural Science Foundation of China (No. 12301423) and the Key Laboratory of Mathematical Model and Application (Guangxi Normal University), Education Department of Guangxi Zhuang Autonomous Region.

References

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