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arXiv · 2310.13658

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

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 Möbius function $μ(n)$ 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 $φ(n)$. Keywords: Lambert series; Möbius function; $q$-series; partition function

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Mircea Merca, Maxie D. Schmidt. 2023-10-20. The partition function $p(n)$ in terms of the classical Möbius function. https://doi.org/10.1007/s11139-017-9988-0

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