Finite Ordered Sets

A comprehensive account that gives equal attention to the combinatorial, logical and applied aspects of partially ordered sets.

As the first book to focus exclusively on finite ordered sets, this book will be welcomed by graduate students and researchers. After defining key concepts and presenting the main results, it describes the many applications of these structures in fields such as preference modelling and aggregation, and data mining.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.