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FURTHER ARITHMETIC PROPERTIES OF OVERCUBIC PARTITION TRIPLES

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  10 January 2025

MANJIL P. SAIKIA Open the ORCID record for MANJIL P. SAIKIA [Opens in a new window]  and
ABHISHEK SARMA Open the ORCID record for ABHISHEK SARMA [Opens in a new window]
MANJIL P. SAIKIA
Affiliation:
Mathematical and Physical Sciences Division, School of Arts and Sciences, Ahmedabad University, Ahmedabad 380009, Gujarat, India e-mail: [email protected]
ABHISHEK SARMA*
Affiliation:
Department of Mathematical Sciences, Tezpur University, Napaam, Tezpur 784028, Assam, India
*
e-mail: [email protected]
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Abstract

We prove several new congruences for the overcubic partition triples function, using both elementary techniques and the theory of modular forms. These extend the recent list of such congruences given by Nayaka, Dharmendra and Kumar [‘Divisibility properties for overcubic partition triples’, Integers 24 (2024), Article no. a80, 9 pages]. We also generalise overcubic partition triples to overcubic partition k-tuples and prove arithmetic properties for these partitions.

Keywords

integer partitionsRamanujan-type congruencesRadu’s algorithmmodular forms

MSC classification

Primary: 11P83: Partitions; congruences and congruential restrictions
Secondary: 11P81: Elementary theory of partitions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 14
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The second author was partially supported by an institutional fellowship for doctoral research from Tezpur University, Assam, India.

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