Oriented Matroids

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Anders Björner (Royal Institute of Technology, Stockholm) Michel Las Vergnas (Laboratoire de Probabilités, Université Pierre et Marie Curie)

Oriented Matroids

Anders Björner (Royal Institute of Technology, Stockholm), Michel Las Vergnas (Laboratoire de Probabilités, Université Pierre et Marie Curie), Bernd Sturmfels (University of California, Berkeley) , Neil White (University of Florida)

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English

Cambridge University Press
14 November 2000

Algebra; Optimisation; Combinatorics & graph theory

Series: Encyclopedia of Mathematics and its Applications

Oriented matroids are a very natural mathematical concept which presents itself in many different guises and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the second edition of the first comprehensive, accessible account of the subject. It is intended for a diverse audience: graduate students who wish to learn the subject from scratch; researchers in the various fields of application who want to concentrate on certain aspects of the theory; specialists who need a thorough reference work; and others at academic points in between. A list of exercises and open problems ends each chapter. For the second edition, the authors have expanded the bibliography greatly to ensure that it remains comprehensive and up-to-date, and they have also added an appendix surveying research since the work was first published.

By: Anders Björner (Royal Institute of Technology Stockholm), Michel Las Vergnas (Laboratoire de Probabilités, Université Pierre et Marie Curie), Bernd Sturmfels (University of California, Berkeley), Neil White (University of Florida), Gunter M. Ziegler (Technische Universität Berlin)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Volume: 46
Dimensions: Height: 235mm, Width: 157mm, Spine: 30mm
Weight: 805g
ISBN: 9780521777506
ISBN 10: 052177750X
Series: Encyclopedia of Mathematics and its Applications
Pages: 564
Publication Date: 14 November 2000
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Preface; Notation; 1. A first orientation session; 2. A second orientation session; 3. Axiomatics; 4. From face lattices to topology; 5. Topological models for oriented matroids; 6. Arrangements of pseudolines; 7. Constructions; 8. Realizability; 9. Convex polytopes; 10. Linear programming; Appendix: Some current frontiers of research; Bibliography; Index.

Reviews for Oriented Matroids

From reviews of the first edition: 'Overall this is a book which is a classic of its type; it is a mine of information, which will be the authoritative source for many years to come.' Bulletin of the London Mathematical Society '... fulfils its purpose as an authoritative and comprehensive reference... as readable a source on oriented matroids as one might imagine.' Zeitschrift fur Operations Research '... comprehensive and up-to-date ...'. L'Enseignement Mathematique