Finite Ordered Sets

Erscheinungsjahr 2019
ISBN: 978-1-107-01369-8
Verlag: Cambridge University Press

Buch, Englisch, Band 144, 350 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 754 g

Reihe: Encyclopedia of Mathematics and its Applications

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.

Autoren/Hrsg.

Caspard, Nathalie

Leclerc, Bruno

Monjardet, Bernard

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

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.

Über Autor(innen)

Monjardet, Bernard
Bernard Monjardet is Emeritus Professor at the Université Paris 1 Panthéon-Sorbonne.

Leclerc, Bruno
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.

Caspard, Nathalie
Nathalie Caspard is an Assistant Professor in the Laboratoire d'Algorithmique, Complexité et Logique (LACL) at Université Paris Est.

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.