Finite Ordered Sets: Concepts, Results and Uses

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Cambridge University Press, Jan 26, 2012 - Mathematics - 337 pages
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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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Contents

A About algorithmic complexity
270
B The 58 types of connected ordered sets of size at most 5
286
C The numbers of ordered sets and of types of ordered sets
288
D Documentation marks
290
References
296
List of symbols
325
Index
329
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About the author (2012)

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

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 is Emeritus Professor at the Université Paris 1 Panthéon-Sorbonne.

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