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    • Publisher:
      Cambridge University Press
      Publication date:
      February 2012
      January 2012
      ISBN:
      9781139005135
      9781107013698
      DOI:
      https://doi.org/10.1017/CBO9781139005135
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.65kg, 350 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Logic, Categories and Sets, Discrete Mathematics Information Theory and Coding
      Series:
      Encyclopedia of Mathematics and its Applications (144)
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    Subjects:
    Mathematics (general), Mathematics, Logic, Categories and Sets, Discrete Mathematics Information Theory and Coding
    Series:
    Encyclopedia of Mathematics and its Applications (144)
    Information

    Book description

    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.

    Reviews

    "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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