Oriented MatroidsOriented 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. |
Contents
1 A First Orientation Session | 1 |
2 A Second Orientation Session | 46 |
3 Axiomatics | 100 |
4 From Face Lattices to Topology | 157 |
5 Topological Models for Oriented Matroids | 225 |
6 Arrangements of Pseudolines | 247 |
7 Constructions | 281 |
Other editions - View all
Oriented Matroids: Second Edition Anders Bjorner,Michel Las Vergnas,Bernd Sturmfels,Günter Ziegler,Anders Bj Rner,Neil L. White No preview available - 1999 |
Common terms and phrases
acyclic adjoint affine affine space algebraic algorithm allowable sequence arrangement of hyperplanes axiom basis Bokowski Bruhat order cell complex cell decomposition chirotope cocircuit combinatorial construction contains Cordovil Corollary corresponding covectors Coxeter Coxeter group defined Definition denote dual duality Edmonds and Mandel equivalent example exists face lattice facets feasible Figure finite geometric Hence homeomorphism homotopy hyperplane arrangement implies induced isomorphic Lemma linear programming M₁ matroid of rank matroid polytope maximal non-realizable optimal oriented matroid program orthogonal pair pivot plane point configuration positive cocircuits problem projective pseudocircles pseudospheres rank 3 oriented realization space regular cell complex reorientation satisfies Section shellable Show sign vectors signed circuits signed set simplex simplex algorithm simplicial simplicial complex single element extension sphere Sturmfels subset T-basis tableau Theorem tope graph topological triangulation underlying matroid uniform oriented matroid Vergnas vertex vertices zonotope