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 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 theory of species. It provides a unified understanding of the use of generating functions for labelled and unlabelled structures. Of particular importance is their capacity to transform recursive definitions into functional or differential equations, and conversely. Applications include graphical enumeration, Polya Theory and analysis of data structures in computer science, 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.