Lagrange inversion for species
type: Item
instance of: scholarly article
title: Lagrange inversion for species
zbMATH Open document ID: 0833.05081
DOI: 10.1016/0097-3165(95)90030-6
author: Ira M. Gessel
author: Gilbert Labelle
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-03-11T00:00:00Z
review text: 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.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05E99
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 802351
zbMATH Keywords: Lagrange power series inversion theorem
zbMATH Keywords: species
zbMATH Keywords: cycle index series
zbMATH Keywords: symmetric functions
zbMATH Keywords: differential operators
zbMATH Keywords: Pólya's theorem
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90030-6
OpenAlex ID: W1978061689
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description: scientific article; zbMATH DE number 802351