Finite Ordered Sets: Concepts, Results and Uses

by Nathalie Caspard, Bruno Leclerc, Bernard Monjardet

Overview

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.

Product Details

ISBN-13:	9781107086777
Publisher:	Cambridge University Press
Publication date:	01/26/2012
Series:	Encyclopedia of Mathematics and its Applications , #144
Sold by:	Barnes & Noble
Format:	eBook
File size:	15 MB
Note:	This product may take a few minutes to download.

About the Author

Nathalie Caspard is an Assistant Professor in the Laboratoire d'Algorithmique, Complexité et Logique (LACL) at Université Paris Est.
Bruno Leclerc is an Honorary Member of the Centre d'Analyse et de Mathématique Sociales of the École des Hautes Études en Sciences Sociales (School of High Studies in Social Sciences) in Paris, and of the CNRS.
Bernard Monjardet is Emeritus Professor at the Université Paris 1 Panthéon-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.