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Finite Ordered Sets
Concepts, Results and Uses

$84.00 ( ) USD

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: August 2013
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781139382625

$ 84.00 USD ( )
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About the Authors
  • Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite ordered sets, this book will be welcomed by graduate students and researchers in all of these areas. Beginning with definitions of key concepts and fundamental results (Dilworth's and Sperner's theorem, interval and semiorders, Galois connection, duality with distributive lattices, coding and dimension theory), the authors then present applications of these structures in fields such as preference modelling and aggregation, operational research and management, cluster and concept analysis, and data mining. Exercises are included at the end of each chapter with helpful hints provided for some of the most difficult examples. The authors also point to further topics of ongoing research.

    • The first book to focus exclusively on finite ordered sets
    • Unique in giving equal attention to the combinatorial, logical and applied aspects of partially ordered sets
    • Discusses applications in various fields
    • Contains over 100 exercises
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    Reviews & endorsements

    "Of special value are the many paragraphs devoted to the historical development of the topics considered with ample citations to the literature on ordered sets from the earliest to the very recent"
    -Joel Berman, Mathematical Reviews

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    Product details

    • Date Published: August 2013
    • format: Adobe eBook Reader
    • isbn: 9781139382625
    • contains: 65 b/w illus. 15 tables 120 exercises
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface
    1. Concepts and examples
    2. Particular classes of ordered sets
    3. Morphisms of ordered sets
    4. Chains and antichains
    5. Ordered sets and distributive lattices
    6. Order codings and dimensions
    7. Some uses
    A. About algorithmic complexity
    B. The 58 non-isomorphic connected ordered sets with at most 5 elements
    C. The numbers of ordered sets and of non-isomorphic ordered sets
    D. Documentation marks
    List of symbols
    Bibliography
    Index.

  • Authors

    Nathalie Caspard, Université Paris-Est Créteil (UPEC)
    Nathalie Caspard is an Assistant Professor in the Laboratoire d'Algorithmique, Complexité et Logique (LACL) at Université Paris Est.

    Bruno Leclerc, Ecole des Hautes Etudes en Sciences Sociales, Paris
    Bruno Leclerc is an Honorary Member of the Centre d'Analyse et de Mathématique Sociales of the École des Hautes Études en Sciences Sociales (School of High Studies in Social Sciences) in Paris, and of the CNRS.

    Bernard Monjardet, Université de Paris I
    Bernard Monjardet is Emeritus Professor at the Université Paris 1 Panthéon-Sorbonne.

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