Finite Ordered Sets : Concepts, Results and Uses

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.

Nathalie Caspard is an Assistant Professor in the Laboratoire d'Algorithmique, Complexite et Logique (LACL) at Universite Paris Est. Bruno Leclerc is an Honorary Member of the Centre d'Analyse et de Mathematique Sociales of the Ecole des Hautes Etudes en Sciences Sociales (School of High Studies in Social Sciences) in Paris, and of the CNRS. Bernard Monjardet is Emeritus Professor at the Universite Paris 1 Pantheon-Sorbonne.