Circuit Admissible Triangulations of Oriented Matroids

Download or read book Circuit Admissible Triangulations of Oriented Matroids written by Jörg Rambau and published by . This book was released on 2000 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "All triangulations of euclidean oriented matroids are of the same PL-homeomorphism type by a result of Anderson. That means all triangulations of euclidean acyclic oriented matroids are PL-homeomorphic to PL-balls and that all triangulations of totally cyclic oriented matroids are PL-homeomorphic to PL-spheres. For non-euclidean oriented matroids this question is wide open. One key point in the proof of Anderson is the following fact: for every triangulation of a euclidean oriented matroid the adjacency graph of the set of all simplices 'intersecting' a segment [p-p+] is a path. We call this graph the [p-p+]-adjacency graph of the triangulation. While we cannot solve the problem of the topological type of triangulations of general oriented matroids we show in this note that for every circuit admissible triangulation of an arbitrary oriented matroid the [p-p+] adjacency graph is path."