Applications of the theory of automata in enumeration (Q1122575)

After an introductory section, the paper contains a discussion of enumeration of reduced words in a finite group action (the discussion does not have any dismembering, there are no emphasized sentences, e.g. theorems). Finally, a new proof is given for \textit{P. A. MacMahon}'s Master Theorem [Combinatory analysis, Vols. I, II (1915/1916, new edition 1960; Zbl 0101.251)] [cf. also \textit{P. Cartier} and \textit{D. Foaţa}, Lect. Notes Math. 85, 54-68 (1969; Zbl 0186.30101)]. This proof uses flows and circuits of directed graphs, as well as semiautomata over commutative rings.