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In search of unity: Galois connections and Möbius-Rota inversions. (Portuguese. English summary) Zbl 1446.06008

Summary: This paper is organized in two distinct but parallel parts. Our goal is to illustrate the parallel between the usefulness of Galois connections (quasi-inversions) in number theory and of Möbius-Rota inversions in enumerative combinatorics. These tools allow to address apparently hard problems in an illuminating unifying way, by (quasi-)inverting them into much simpler equivalent problems. The common setting is the conceptual point of view of lattice theory.

MSC:

06A15 Galois correspondences, closure operators (in relation to ordered sets)
05A15 Exact enumeration problems, generating functions
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