Finite Ordered Sets : Concepts, Results and Uses / [electronic resource]
by Caspard, Nathalie [author.]; Leclerc, Bruno [author.]; Monjardet, Bernard [author.].
Material type:
BookSeries: Encyclopedia of Mathematics and its Applications ; no. 144.Publisher: Cambridge : Cambridge University Press, 2012.Description: 1 online resource (350 pages) : digital, PDF file(s).ISBN: 9781139005135 (ebook).Subject(s): Ordered sets | Finite groupsOnline resources: Cambridge Books Online 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.
Title from publisher's bibliographic system (viewed on 09 Oct 2015).
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.
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