Finite ordered sets
By: Nathalie Caspard, Bruno Leclerc, Bernard Monjardet
Contributors: Leclerc, Bruno; Monjardet, Bernard, 1938-
Series: Encyclopedia of mathematics and its applications -- 144
Publisher: Cambridge University Press
Published: 2012
Place of publication: Cambridge; New York
Language: eng
ISBN-13: 9781107013698
Subjects: Finite groups; MATHEMATICS / Discrete Mathematics; Ordered sets
Description: "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"--
Notes: Includes bibliographical references and index.
Table of contents: title: Machine generated contents note: 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.