Combinatorial Species and Tree-like Structures (Encyclopedia of Mathematics and its Applications, Series Number 67)

The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the specification and analysis of these structures. Of particular importance is their capacity to transform recursive definitions of tree-like structures into functional or differential equations, and vice versa. The goal of this book is to present the basic elements of the theory and to give a unified account of its developments and applications. It offers a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis and differential equations. This book will be a valuable reference to graduate students and researchers in combinatorics, analysis, and theoretical computer science. The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labeled and unlabeled structures as well as a tool for the specification and analysis of these structures. This key reference presents the basic elements of the theory and gives a unified account of its developments and applications. The authors offer a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya Theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis, and differential equations. This book is the first complete presentation in English of the combinatorial theory of species, introduced by A. Joyal in 1980. It gives a unified understanding of the use of generating functions for both labeled and unlabeled structures and also provides a tool for the specification and analysis of these structures. Of particular importance is the capacity of combinatorial species to transform recursive definitions of tree-like structures into functional or differential equations, and conversely