Oriented Matroids

First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.

Anders Björner (Author), Michel Las Vergnas (Author), Bernd Sturmfels (Author), Neil White (Author), Gunter M. Ziegler (Author)

9780521777506, Cambridge University Press

Paperback, published 18 November 1999

564 pages, 299 exercises
23.5 x 15.7 x 3 cm, 0.805 kg

'… comprehensive and up-to-date …'. L'Enseignement Mathématique

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.

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.

Subject Areas: Combinatorics & graph theory [PBV], Optimization [PBU]