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  3. Combinatorial Species and Tree-like Structures
  • Cited by 87
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2013
      November 1997
      ISBN:
      9781107325913
      9780521573238
      DOI:
      https://doi.org/10.1017/CBO9781107325913
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.8kg, 480 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding
      Series:
      Encyclopedia of Mathematics and its Applications (67)
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    Subjects:
    Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding
    Series:
    Encyclopedia of Mathematics and its Applications (67)
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    Book description

    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.

    Reviews

    ‘This book can serve as an introduction to the subject; it will also be an extremely valuable reference book.’

    Source: International Mathematical News

    ‘ … the first complete presentation in English of the combinatorial theory of species.’

    Source: L’Enseignment Mathématique

    ‘ … a comprehensive account.’

    Source: Zentralblatt für Mathematik und ihre Grenzgebiete

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