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CONGRUENCES FOR RANKS OF PARTITIONS

Published online by Cambridge University Press:  29 January 2024

RENRONG MAO*
Affiliation:
Department of Mathematics, Soochow University, Suzhou 215006, PR China

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.

Type
Research Article
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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