California State University, Northridge WordmarkOviatt Library WordmarkOviatt Library Catalog Wordmark
Author Caspard, Nathalie.
Title Finite ordered sets : concepts, results and uses / Nathalie Caspard, Bruno Leclerc, Bernard Monjardet.
Published Cambridge ; New York : Cambridge University Press, 2012.
Book Cover
 Floor4  QA171.48 .C374 2012    IN LIBRARY
Description xi, 337 p. : ill. ; 24 cm.
Series Encyclopedia of mathematics and its applications ; 144
Encyclopedia of mathematics and its applications ; v. 144.
Bibliography Includes bibliographical references (p. [296]-324) and index.
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 types of connected sets of size at most 5 -- C. The numbers of ordered sets and types of ordered sets -- D. Documentation marks.
Summary "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"-- Provided by publisher.
Subject Ordered sets.
Finite groups.
Related Names Leclerc, Bruno.
Monjardet, Bernard, 1938-
ISBN 1107013690 (hardback)
9781107013698 (hardback)
OCLC number 758844614