Finite Ordered Sets
Concepts, Results and Uses

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

Nathalie Caspard (Author), Bruno Leclerc (Author), Bernard Monjardet (Author)

9781107013698, Cambridge University Press

Hardback, published 26 January 2012

350 pages, 65 b/w illus. 15 tables 120 exercises
24 x 16.5 x 2.1 cm, 0.65 kg

"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

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.

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.

Subject Areas: Optimization [PBU], Discrete mathematics [PBD], Set theory [PBCH], Mathematical logic [PBCD]