The partition function $p(n)$ in terms of the classical M\"{o}bius function

Mircea Merca; Maxie D. Schmidt

doi:10.1007/s11139-017-9988-0

The partition function $p(n)$ in terms of the classical M\"{o}bius function

Combinatorics 2023-10-23 v1 Number Theory

Authors: Mircea Merca , Maxie D. Schmidt

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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 M\"{o}bius 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 $\varphi(n)$ . Keywords: Lambert series; M\"{o}bius function; $q$ -series; partition function

Keywords

partition theory partition congruences special functions

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@article{arxiv.2310.13658,
  title  = {The partition function $p(n)$ in terms of the classical M\"{o}bius function},
  author = {Mircea Merca and Maxie D. Schmidt},
  journal= {arXiv preprint arXiv:2310.13658},
  year   = {2023}
}

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Preprint version of the article submitted in December of 2017

The partition function $p(n)$ in terms of the classical M\"{o}bius function

Abstract

Keywords

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