Finite Ordered Sets

Concepts, Results and Uses

By: Nathalie Caspard, Bruno Leclerc, Bernard Monjardet

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Hardcover | 26 January 2012

At a Glance

Hardcover
350 Pages

Dimensions(cm)
23.39 x 15.6 x 2.39

Hardcover

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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.

Industry 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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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Set Theory Discrete Mathematics Optimisation

Preface
Concepts and examples
Particular classes of ordered sets
Morphisms of ordered sets
Chains and antichains
Ordered sets and distributive lattices
Order codings and dimensions
Some uses
About algorithmic complexity
The 58 non-isomorphic connected ordered sets with at most 5 elements
The numbers of ordered sets and of non-isomorphic ordered sets
Documentation marks
List of symbols
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

Finite Ordered Sets

Concepts, Results and Uses

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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