Finite Ordered Sets
Concepts, Results and Uses
£87.99
Part of Encyclopedia of Mathematics and its Applications
- Authors:
- Nathalie Caspard, Université Paris-Est Créteil (UPEC)
- Bruno Leclerc, Ecole des Hautes Etudes en Sciences Sociales, Paris
- Bernard Monjardet, Université de Paris I
- Date Published: January 2012
- availability: Available
- format: Hardback
- isbn: 9781107013698
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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.
Read more- The first book to focus exclusively on finite ordered sets
- Unique in giving equal attention to the combinatorial, logical and applied aspects of partially ordered sets
- Discusses applications in various fields
- Contains over 100 exercises
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×Product details
- Date Published: January 2012
- format: Hardback
- isbn: 9781107013698
- length: 350 pages
- dimensions: 240 x 165 x 21 mm
- weight: 0.65kg
- contains: 65 b/w illus. 15 tables 120 exercises
- availability: Available
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.
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