Combinatorial applications of Möbius inversion

Jameson, Marie; Schneider, Robert

doi:10.1090/S0002-9939-2014-12020-X

Combinatorial applications of Möbius inversion
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by Marie Jameson and Robert P. Schneider

Proc. Amer. Math. Soc. 142 (2014), 2965-2971

DOI: https://doi.org/10.1090/S0002-9939-2014-12020-X

Published electronically: May 12, 2014

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Abstract:

In important work on the parity of the partition function, Ono (2010) related values of the partition function to coefficients of a certain mock theta function modulo 2. In this paper, we use Möbius inversion to give analogous results which relate several combinatorial functions via identities rather than congruences.

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