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.
- Electronic book text
- 02 Aug 2013
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
- 65 b/w illus. 15 tables 120 exercises
About Nathalie Caspard
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.
Table of contents
Preface; 1. Concepts and examples; 2. Particular classes of ordered sets; 3. Morphisms of ordered sets; 4. Chains and antichains; 5. Ordered sets and distributive lattices; 6. Order codings and dimensions; 7. Some uses; A. About algorithmic complexity; B. The 58 non-isomorphic connected ordered sets with at most 5 elements; C. The numbers of ordered sets and of non-isomorphic ordered sets; D. Documentation marks; List of symbols; Bibliography; Index.
"Of special value are the many paragraphs devoted to the historical development of the topics considered with ample citations to the literature on ordered sets from the earliest to the very recent" -Joel Berman, Mathematical Reviews