Finite ordered sets : concepts, results and uses /
Caspard, Nathalie.
Finite ordered sets : concepts, results and uses / Nathalie Caspard, Bruno Leclerc, Bernard Monjardet. - xi, 337 pages : illustrations ; 24 cm - Encyclopedia of mathematics and its applications ; 144. . - Encyclopedia of mathematics and its applications ; v. 144. .
Includes bibliographical references and index.
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 elements; C. The numbers of ordered sets and types of ordered sets; D. Documentation marks; List of symbols; Bibliography; Index.
"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"--
1107013690 (hardback) 9781107013698 (hardback)
2011040516
Ordered sets.
Finite groups.
QA171.48 / .C374 2012
511.32 / C.N.F
Finite ordered sets : concepts, results and uses / Nathalie Caspard, Bruno Leclerc, Bernard Monjardet. - xi, 337 pages : illustrations ; 24 cm - Encyclopedia of mathematics and its applications ; 144. . - Encyclopedia of mathematics and its applications ; v. 144. .
Includes bibliographical references and index.
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 elements; C. The numbers of ordered sets and types of ordered sets; D. Documentation marks; List of symbols; Bibliography; Index.
"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"--
1107013690 (hardback) 9781107013698 (hardback)
2011040516
Ordered sets.
Finite groups.
QA171.48 / .C374 2012
511.32 / C.N.F