Lagrange inversion for species
The authors give a combinatorial proof of the Lagrange power series inversion theorem for species (according to A. Joyal's theory), derived from G. Labelle's analogous theorem for cycle index series (or, equivalently, symmetric functions); see \textit{A. Joyal} [Combinatoire énumérative, Proc. Colloq., Montreal/Can. 1985, Lect. Notes Math. 1234, 126-159 (1986; Zbl 0612.18002)]. Several new operations on species are discussed that correspond to operations on cycle index series, including differential operators and De Bruijn's generalization of Pólya's theorem.
scientific article; zbMATH DE number 802351
scientific article