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008 210816b ||||| |||| 00| 0 eng d
020 _a9781139005135
041 _aeng.
082 _a511.32
100 1 _aCaspard, Nathalie.
_eauthor
245 _aFinite ordered sets :
_bconcepts, results and uses /
_cNathalie Caspard, Bruno Leclerc, Bernard Monjardet.
264 1 _aCambridge:
_bCambridge University Press,
_cc2012
300 _a1 online resource (350 pages) :
336 _2rdacontent
_atext
_btext
337 _2rdamedia
_acomputer
_bc
338 _2rdacarrier
_aonline resource
_bcr
504 _aIncludes bibliographical references and index.
505 _aPreface; 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.
520 _a"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.
650 0 _aOrdered sets.
650 0 _aFinite groups.
655 0 _aElectronic books.
700 1 _aLeclerc, Bruno.
700 1 _aMonjardet, Bernard.
_d1938-
856 _yFull text available at Cambridge University Press Click here to view
_uhttps://www.cambridge.org/core/books/finite-ordered-sets/6694B691D33BCF13AA17F28FA7C47EE6
942 _2ddc
_cER