Finite Ordered Sets Concepts, Results and Uses

Nathalie Caspard (), Bruno Leclerc and Bernard Monjardet
Additional contact information
Nathalie Caspard: LACL - Laboratoire d'Algorithmique Complexité et Logique - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique
Bruno Leclerc: CAMS - Centre d'Analyse et de Mathématique sociales - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

Abstract: Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. We present the first book to dealing exclusively with finite ordered sets. Five chapters are devoted to definitions of key concepts and fundamental results (ranked orders, Dilworth's and Sperner's theorem, Galois connection and residuation, duality between orders and distributive lattices, coding and dimension theory). The last - and larger - chapter presents uses 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 or references provided for the most difficult ones. We also point to further topics of ongoing research. At last there are appendices devoted to algorithmic complexity, documentation marks, types and numbers of ordered sets, about 500 references, a list of symbols and a (substantial) index.

Keywords: Sperner's theorem; ordered set; Sperner's theorem .; Galois connection; implicational system; interval order; order dimension; distributive lattice; Dilworth's theorem; cluster analysis; chain; coding; Arrow's theorem; antichain; analyse des données; antichaîne; chaîne; codage; correspondance de Galois; dimension; implication; ordre; ordre d'intervalle; théorème d'Arrow; théorème de Dilworth; théorème de Sperner; treillis distributif. (search for similar items in EconPapers)
Date: 2012-01
References: Add references at CitEc
Citations: View citations in EconPapers (18)

Published in Cambridge University Press, pp.337, 2012

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
Working Paper: Finite Ordered Sets Concepts, Results and Uses (2012)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00800193

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().