Invertibility of binary functions (Q1324907)

Various generalizations of Hall's formula for computing the Moebius function of locally finite \(f\)-acyclic binary relations were proved by various authors. It was noted by \textit{B. S. Stechkin} [Tr. Mat. Inst. Steklova 143, 178-187 (1977; Zbl 0442.06001)] that these generalizations are valid for certain binary relations that are not \(f\)-acyclic; in the present paper we propose a generalization of Hall's formula that explains this phenomenon.