Finite Ordered Sets : Concepts, Results and Uses / Nathalie Caspard, Bruno Leclerc, Bernard Monjardet.

Title from publishers bibliographic system (viewed 15 Feb 2012).

Available through Cambridge books online SHEDL trial from 9th January 2012 to June 2012.

A comprehensive account that gives equal attention to the combinatorial, logical and applied aspects of partially ordered sets.

Cover; Half-title; Title; Copyright; Contents; Preface; 1 Concepts and examples; 1.1 Ordered sets; 1.1.1 Orders and strict orders; 1.1.2 Graphs associated with an ordered set; 1.1.3 Diagram of an ordered set; 1.1.4 Isomorphism and duality; 1.2 Examples of uses; 1.2.1 Mathematics; 1.2.2 Biology; 1.2.3 Computer science; 1.2.4 Social sciences; 1.2.5 Operations research; 1.3 Ordered subsets and extensions; 1.3.1 Ordered subsets; 1.3.2 Chains, antichains, and associated parameters; 1.3.3 Extensions; 1.4 Particular elements and subsets; 1.4.1 Meets, joins, and irreducible elements.

1.4.2 Downsets and upsets (ideals and filters)1.5 Constructing ordered sets from given ones; 1.5.1 Substitution, disjoint union, linear sum, lexicographic product; 1.5.2 Direct product; 1.6 Further topics and references; 1.7 Exercises; 2 Particular classes of ordered sets; 2.1 Ranked, semimodular, and bipartite ordered sets; 2.2 Ordered sets with forbidden configurations; 2.3 Semilattices and lattices; 2.4 Linearly ordered sets and tournaments; 2.5 Further topics and references; 2.6 Exercises; 3 Morphisms of ordered sets; 3.1 Isotone and antitone maps: exponentiation.

3.2 Join- and meet-generating sets3.3 Closure and dual closure operators; 3.4 Residuated, residual, and Galois maps; 3.5 The Galois connection associated with a binary relation; 3.5.1 Galois lattice; 3.5.2 Table of an ordered set; 3.5.3 Completion of an ordered set; 3.6 Further topics and references; 3.7 Exercises; 4 Chains and antichains; 4.1 Dilworth's decomposition theorem; 4.2 Matchings and transversals in a bipartite ordered set; 4.3 The Sperner property; 4.4 Direct products of chains; 4.5 Further topics and references; 4.6 Exercises; 5 Ordered sets and distributive lattices.

5.1 Distributive lattices5.2 The distributive lattice associated with an ordered set; 5.3 Representations of a distributive lattice; 5.4 Dualities: preorders-topologies, orders-distributive lattices; 5.5 Duality between orders and spindles of linear orders; 5.6 Further topics and references; 5.7 Exercises; 6 Order codings and dimensions; 6.1 Boolean codings and Boolean dimension of an ordered set; 6.2 Dimension of an ordered set; 6.3 2-dimensional ordered sets; 6.4 k-dimension of an ordered set; 6.5 Further topics and references; 6.6 Exercises; 7 Some uses; 7.1 Models of preferences.

7.2 Preference aggregation: Arrowian theorems for orders7.3 The roles of orders in cluster analysis; 7.4 Implicational systems, Moore families and Galois data analysis; 7.5 Orders in scheduling; 7.5.1 The single-machine scheduling problem; 7.5.2 The m-machine scheduling problem; 7.5.3 The two-step (and two-machine) scheduling problem; 7.6 Further topics and references; 7.6.1 Preference models; 7.6.2 Preference aggregation: Arrowian theorems for orders; 7.6.3 The roles of orders in cluster analysis; 7.6.4 Implicational systems, Moore families, and Galois data analysis.

Includes bibliographical references (pages 296-324) and index.

English.

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