Combinatorial Species and Tree-like Structures: 67 (Encyclopedia of Mathematics and its Applications, Series Number 67)
Cambridge University Press, 12/11/1997
EAN 9780521573238, ISBN10: 0521573238
Hardcover, 480 pages, 24.8 x 17.1 x 3.2 cm
Language: English
Originally published in French, translated by Margaret Readdy
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.
1. Introduction to species of structures
2. Complements on species of structures
3. Combinatorial functional equations
4. Complements on types of structures
5. Species on totally ordered sets.