Circuit Admissible Triangulations of Oriented Matroids |
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Authors: | J Rambau |
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Institution: | Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustra?e 7, 14195 Berlin, Germany rambau@zib.de, DE
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Abstract: | 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.
Received December 8, 2000, and in revised form May 23, 2001. Online publication November 7, 2001. |
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