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  1. Home
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  3. Finite Ordered Sets
  • Cited by 34
Publisher:
Cambridge University Press
Online publication date:
February 2012
Print publication year:
2012
Online ISBN:
9781139005135
DOI:
https://doi.org/10.1017/CBO9781139005135
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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