Finite Ordered Sets

Concepts, Results and Uses

Nonfiction, Science & Nature, Mathematics, Discrete Mathematics, Logic
Cover of the book Finite Ordered Sets by Nathalie Caspard, Bruno Leclerc, Bernard Monjardet, Cambridge University Press
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Author: Nathalie Caspard, Bruno Leclerc, Bernard Monjardet ISBN: 9781107086777
Publisher: Cambridge University Press Publication: January 26, 2012
Imprint: Cambridge University Press Language: English
Author: Nathalie Caspard, Bruno Leclerc, Bernard Monjardet
ISBN: 9781107086777
Publisher: Cambridge University Press
Publication: January 26, 2012
Imprint: Cambridge University Press
Language: English

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.

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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.

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