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CONGRUENCES FOR RANKS OF PARTITIONS

Part of: Discontinuous groups and automorphic forms Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  29 January 2024

RENRONG MAO
RENRONG MAO*
Affiliation:
Department of Mathematics, Soochow University, Suzhou 215006, PR China
*
e-mail: [email protected]
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Abstract

Ranks of partitions play an important role in the theory of partitions. They provide combinatorial interpretations for Ramanujan’s famous congruences for partition functions. We establish a family of congruences modulo powers of $5$ for ranks of partitions.

Keywords

partitionsrankscongruencesmodular functions

MSC classification

Primary: 11P83: Partitions; congruences and congruential restrictions
Secondary: 05A17: Partitions of integers 11F30: Fourier coefficients of automorphic forms 11F37: Forms of half-integer weight; nonholomorphic modular forms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 110 , Issue 2 , October 2024 , pp. 280 - 290
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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

This work is supported by NSFC (National Natural Science Foundation of China) through Grant No. NSFC 12071331.

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