Combinatorial Species and Tree-like Structures

François Bergeron, Gilbert Labelle, Pierre Leroux, Margaret Readdy

• Publisher: Cambridge University Press
• Year: 1997
• ISBN:
  9781107108776
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the specification and analysis of these structures. Of particular importance is their capacity to transform recursive definitions of tree-like structures into functional or differential equations, and vice versa. The goal of this book is to present the basic elements of the theory and to give a unified account of its developments and applications. It offers 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 will be a valuable reference to graduate students and researchers in combinatorics, analysis, and theoretical computer science.

Table of contents

• Cover
• Half Title
• Title
• Copyright
• Foreword
• Table of Contents
• Preface
• 1 Introduction to Species of Structures
• 2 Complements on Species of Structure
• 3 Combinatorial Functional Equations
• 4 Complements on Unlabeled Enumeration
• 5 Species on Totally Ordered Sets
• Appendix 1: Group Actions and Pólya Theory
• Appendix 2: Miscellaneous Tables
• Bibliography
• Notation Index
• Index