Combinatorial Species and Tree-like Structures

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Cambridge University Press, 1998 - Mathematics - 457 pages
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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
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