Combinatorial Species and Tree-like Structures

Foreword page v
Preface xi
1 Introduction to Species of Structures 1
1.0 Introduction 1
1.1 Notion of Species of Structures 1
1.2 Associated Series 12
1.3 Addition and Multiplication 26
1.4 Substitution and Differentiation 40
2 Complements on Species of Structures 59
2.0 Introduction 59
2.1 Pointing and Cartesian Product 60
2.2 Functorial Composition 70
2.3 Weighted Species 79
2.4 Extension to the Multisort Context 100
2.5 Virtual Species 120
2.6 Molecular and Atomic Species 139
3 Combinatorial Functional Equations 162
3.0 Introduction 162
3.1 Lagrange Inversion 164
3.2 Implicit Species Theorem 191
3.3 Quadratic Iterative Methods 222
3.4 Elements of Asymptotic Analysis 247
4 Complements on Unlabeled Enumeration 277
4.0 Introduction 277
4.1 The Dissymmetry Theorem for Trees 278
4.2 Connected Graphs and Blocks 297
4.3 Proof of the Substitution Formulas 309
4.4 Asymmetric Structures 321
5 Species on Totally Ordered Sets 341
5.0 Introduction 341
5.1 L-Species 342
5.2 Combinatorial Differential Equations 358
Appendix 1: Group Actions and Polya Theory 393
Appendix 2: Miscellaneous Tables 408
Bibliography 434
Notation Indexx 447
Index 449