nLab Combinatorial species and tree-like structures

This is a page about a major book on combinatorial species and about its sequel.

• F. Bergeron, G. Labelle and P. Leroux, Combinatorial species and tree-like structures, Enc. of Math. and its Appl., Camb. Univ. Press 1997

which is a corrected translation from French

• François Bergeron, Gilbert Labelle, Pierre Leroux, Théorie des espèces et combinatoire des structures arborescentes, LaCIM, Montréal (1994).

• bookpage

• Preface by Gian-Carlo Rota (pdf, ps.gz)

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

New book

• F. Bergeron, G. Labelle, P. Leroux, Introduction to the Theory of Species of Structures 2008, pdf

category: reference