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A NEW REFINEMENT OF FINE’S PARTITION THEOREM

Published online by Cambridge University Press:  29 March 2021

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

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.

Type
Research Article
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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References

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Yee, A. J., ‘Bijective proof of a theorem of Fine and related partition identities’, Int. J. Number Theory 5 (2009), 219228.CrossRefGoogle Scholar

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