New infinite hierarchies of polynomial identities related to the Capparelli partition theorems

Alexander Berkovich; Ali Kemal Uncu

doi:10.1016/j.jmaa.2021.125678

New infinite hierarchies of polynomial identities related to the Capparelli partition theorems

Alexander Berkovich, Ali Kemal Uncu

Research output: Contribution to journal › Article › peer-review

1 Citation (SciVal)

Abstract

We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also discuss the q↦1/q duality transformation of the base identities and some related partition theoretic relations.

Original language	English
Article number	125678
Journal	Journal of Mathematical Analysis and Applications
Volume	506
Issue number	2
Early online date	21 Sept 2021
DOIs	https://doi.org/10.1016/j.jmaa.2021.125678
Publication status	Published - 15 Feb 2022

Bibliographical note

Funding Information:
The second author would like to send gratitude to EPSRC grant number EP/T015713/1 and partly by FWF grant P-34501-N for supporting his work.

Funding Information:
Research of the second author is partly supported by EPSRC grant number EP/T015713/1 and partly by FWF grant P-34501-N.The authors would like to thank Krishnaswami Alladi, George E. Andrews, Peter Paule, and Wadim Zudilin for their genuine interest, encouragement, and helpful comments. The authors would also like to thank the anonymous referee for their careful reading and suggestions. The second author would like to send gratitude to EPSRC grant number EP/T015713/1 and partly by FWF grant P-34501-N for supporting his work.

Keywords

Bailey's lemma
Capparelli's identities
Infinite hierarchies of q-series identities
q-binomial identities

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2021.125678

Cite this

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title = "New infinite hierarchies of polynomial identities related to the Capparelli partition theorems",

abstract = "We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also discuss the q↦1/q duality transformation of the base identities and some related partition theoretic relations.",

keywords = "Bailey's lemma, Capparelli's identities, Infinite hierarchies of q-series identities, q-binomial identities",

author = "Alexander Berkovich and Uncu, {Ali Kemal}",

note = "Funding Information: The second author would like to send gratitude to EPSRC grant number EP/T015713/1 and partly by FWF grant P-34501-N for supporting his work. Funding Information: Research of the second author is partly supported by EPSRC grant number EP/T015713/1 and partly by FWF grant P-34501-N.The authors would like to thank Krishnaswami Alladi, George E. Andrews, Peter Paule, and Wadim Zudilin for their genuine interest, encouragement, and helpful comments. The authors would also like to thank the anonymous referee for their careful reading and suggestions. The second author would like to send gratitude to EPSRC grant number EP/T015713/1 and partly by FWF grant P-34501-N for supporting his work. ",

year = "2022",

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doi = "10.1016/j.jmaa.2021.125678",

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AU - Uncu, Ali Kemal

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PY - 2022/2/15

Y1 - 2022/2/15

N2 - We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also discuss the q↦1/q duality transformation of the base identities and some related partition theoretic relations.

AB - We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also discuss the q↦1/q duality transformation of the base identities and some related partition theoretic relations.

KW - Bailey's lemma

KW - Capparelli's identities

KW - Infinite hierarchies of q-series identities

KW - q-binomial identities

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U2 - 10.1016/j.jmaa.2021.125678

DO - 10.1016/j.jmaa.2021.125678

M3 - Article

AN - SCOPUS:85115439653

SN - 0022-247X

VL - 506

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JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 125678

ER -

New infinite hierarchies of polynomial identities related to the Capparelli partition theorems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Pushing Back the Doubly-Exponential Wall of Cylindrical Algebraic Decomposition

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New infinite hierarchies of polynomial identities related to the Capparelli partition theorems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

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Pushing Back the Doubly-Exponential Wall of Cylindrical Algebraic Decomposition

Cite this