The partition function p(n) in terms of the classical M\"obius function
Abstract
In this paper, we investigate decompositions of the partition function p(n) from the additive theory of partitions considering the famous M\"obius 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 (n). Keywords: Lambert series; M\"obius function; q-series; partition function
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