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A NEW REFINEMENT OF FINE’S PARTITION THEOREM

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  29 March 2021

JIAYU KANG Open the ORCID record for JIAYU KANG [Opens in a new window] ,
RUNQIAO LI Open the ORCID record for RUNQIAO LI [Opens in a new window]  and
ANDREW Y. Z. WANG Open the ORCID record for ANDREW Y. Z. WANG [Opens in a new window]
JIAYU KANG
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu611731, P.R. China e-mail: jiayukang@hotmail.com
RUNQIAO LI
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu611731, P.R. China e-mail: runqiaoli@outlook.com
ANDREW Y. Z. WANG*
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu611731, P.R. China
*
e-mail: yzwang@uestc.edu.cn
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Abstract

We find a new refinement of Fine’s partition theorem on partitions into distinct parts with the minimum part odd. As a consequence, we obtain two companion partition identities. Both analytic and combinatorial proofs are provided.

Keywords

Fine’s partition theoreminvolutionminimal odd excludant

MSC classification

Primary: 05A17: Partitions of integers
Secondary: 11P81: Elementary theory of partitions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 353 - 361
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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References

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