# Combinatorial Species and Tree-like Structures

Cambridge University Press, 1998 - Mathematics - 457 pages
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.

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### Contents

 Introduction to Species of Structures 1 Complements on Species of Structures 59 Combinatorial Functional Equations 162 Complements on Unlabeled Enumeration 277 Species on Totally Ordered Sets 341
 Group Actions and Polya Theory 393 Miscellaneous Tables 408 Bibliography 434 Notation Indexx 447 Copyright