Circuit Admissible Triangulations of Oriented Matroids

All triangulations of euclidean oriented matroids are of the same PL-homeo-morphism 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 t...

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Bibliographic Details
Published in:Discrete & computational geometry 2002-01, Vol.27 (1), p.155-161
Main Author: Rambau, J
Format: Article
Language:English
Subjects:
Circuits
Combinatorics
Computational geometry
Geometry
Graphs
Proving
Segments
Topology
Triangulation
Online Access:Get full text
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Summary:All triangulations of euclidean oriented matroids are of the same PL-homeo-morphism 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 a path. [PUBLICATION ABSTRACT]
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-001-0058-3