Finite Ordered Sets

Concepts, Results and Uses

AvNathalie Caspard,Bruno Leclerc

Inbunden, Engelska, 2012

Del 144 i serien Encyclopedia of Mathematics and its Applications

1 312 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2012-01-26
Mått:165 x 240 x 21 mm
Vikt:650 g
Format:Inbunden
Språk:Engelska
Serie:Encyclopedia of Mathematics and its Applications
Antal sidor:350
Förlag:Cambridge University Press
ISBN:9781107013698

Utforska kategorier

Matematikens grunder inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

"Of special value are the many paragraphs devoted to the historical development of the topics considered with ample citations to the literature on ordered sets from the earliest to the very recent" -Joel Berman, Mathematical Reviews

Innehållsförteckning

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.