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. We present the first book to dealing exclusively with finite ordered sets. Five chapters are devoted to definitions of key concepts and fundamental results (ranked orders, Dilworth's and Sperner's theorem, Galois connection and residuation, duality between orders and distributive lattices, coding and dimension theory). The last - and larger - chapter presents uses 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 or references provided for the most difficult ones. We also point to further topics of ongoing research. At last there are appendices devoted to algorithmic complexity, documentation marks, types and numbers of ordered sets, about 500 references, a list of symbols and a (substantial) index.