Finite Ordered Sets : Concepts, Results and Uses / [electronic resource] Nathalie Caspard, Bruno Leclerc, Bernard Monjardet. Caspard, Nathalie, author. Leclerc, Bruno, author. Monjardet, Bernard, author. Ordered sets Finite groups QA171.48 .C374 2012 511.3/2 23 Title from publisher's bibliographic system (viewed on 09 Oct 2015). 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. 2012 Text 1 online resource (350 pages) : http://dx.doi.org/10.1017/CBO9781139005135 eng Encyclopedia of Mathematics and its Applications ; no. 144 Encyclopedia of Mathematics and its Applications ; no. 144.