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The partition function p(n) in terms of the classical Möbius function

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Abstract

In this paper, we investigate decompositions of the partition function p(n) from the additive theory of partitions considering the famous Möbius function \(\mu (n)\) from multiplicative number theory. Some combinatorial interpretations are given in this context. Our work extends several analogous identities proved recently relating p(n) and Euler’s totient function \(\varphi (n)\).

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Acknowledgements

The authors thank the referees for their helpful comments.

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Authors and Affiliations

  1. Academy of Romanian Scientists, Splaiul Independentei 54, 050094, Bucharest, Romania

    Mircea Merca

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Maxie D. Schmidt

Authors
  1. Mircea Merca
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  2. Maxie D. Schmidt
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Correspondence to Mircea Merca.

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Merca, M., Schmidt, M.D. The partition function p(n) in terms of the classical Möbius function. Ramanujan J 49, 87–96 (2019). https://doi.org/10.1007/s11139-017-9988-0

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  • DOI: https://doi.org/10.1007/s11139-017-9988-0

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