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.
| ISBN: | 9781107013698 |
| Publication date: | 26th January 2012 |
| Author: | Nathalie Caspard, Bruno Ecole des Hautes Etudes en Sciences Sociales, Paris Leclerc, Bernard Université de Paris Monjardet |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 350 pages |
| Series: | Encyclopedia of Mathematics and its Applications |
| Genres: |
Set theory |
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.
Finite Ordered Sets features in the following genres: Set theory
Finite Ordered Sets is available in Hardback
Finite Ordered Sets was written by Nathalie Caspard, Bruno Ecole des Hautes Etudes en Sciences Sociales, Paris Leclerc, Bernard Université de Paris Monjardet and published by Cambridge University Press
Finite Ordered Sets has 350 pages
Yes it is part of Encyclopedia of Mathematics and its Applications series
£87.30