Combinatorial Species and Tree-like Structures     Bergeron, F., Labelle, G. and Leroux, P. 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.

Foreword by Gian-Carlo Rota  (.ps.gz)  (.pdf) Table of Contents 1 Introduction to Species of Structures 1.1 Notion of Species of Structures 1.2 Associated Series 1.3 Addition and Multiplication 1.4 Substitution and Differentiation 2. Complements on Species of Structures 2.1 Pointing and Cartesian Product 2.2 Functorial Composition 2.3 Weighted Species 2.4 Extension to Multisort Context 2.5 Virtual Species 2.6 Molecular and Atomic Species

3. Combinatorial Functional Equations 3.1 Lagrange Inversion 3.2 Implicit Species Theorem 3.3 Quadratic Iterative Methods 3.4 Elements of Asymptotic Analysis 4. Complements on Unlabeled Enumeration 4.1 The Dissymmetry Theorem for Trees 4.2 Connected Graphs and Blocks 4.3 Proof of the Substitution Formula 4.4 Asymmetric Structures 5. Species on Totally Ordered Sets 5.1 L-Species 5.2 Combinatorial Differential Equations Appendix 1: Group Action and Polya Theory Appendix 2: Miscellaneous Tables