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Combinatorial Species and Tree-like Structures

Combinatorial Species and Tree-like Structures

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: February 1998
  • availability: Available
  • format: Hardback
  • isbn: 9780521573238

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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 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.

    • A clear and modern explanation of when to use the different types of generating series
    • Over 350 exercises of varied difficulty
    • Results are summarised into tables of species and associated generating species
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    Reviews & endorsements

    'This book can serve as an introduction to the subject; it will also be an extremely valuable reference book.' International Mathematical News

    ' … the first complete presentation in English of the combinatorial theory of species.' L'Enseignment Mathématique

    ' … a comprehensive account.' Zentralblatt für Mathematik und ihre Grenzgebiete

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    Product details

    • Date Published: February 1998
    • format: Hardback
    • isbn: 9780521573238
    • length: 480 pages
    • dimensions: 243 x 162 x 32 mm
    • weight: 0.8kg
    • contains: 135 b/w illus. 19 tables
    • availability: Available
  • Table of Contents

    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.

  • Authors

    François Bergeron, Université du Québec, Montréal

    Gilbert Labelle, Université du Québec, Montréal

    Pierre Leroux, Université du Québec, Montréal

    Translator

    Margaret Readdy

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