Circuit Admissible Triangulations of Oriented Matroids

Circuit Admissible Triangulations of Oriented Matroids

All triangulations of euclidean oriented matroids are of the same PLhomeomorphism 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 PLspheres. For non-euclidean oriented matroids this question is wide open. One key point in the p...

Circuit Admissible Triangulations of Oriented Matroids Jörg Rambau

All triangulations of euclidean oriented matroids are of the same PLhomeomorphism 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 PLspheres. For non-euclidean oriented matroids this question is wide open. One key point in the p...

Triangulations of Oriented Matroids

We consider the concept of triangulation of an oriented matroid. We provide a de nition which generalizes the previous ones by Billera{ Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroidM and extensions of its dualM , via the so-called lift...

Computing Triangulations Using Oriented Matroids

Triangulations of ∆n−1 ×∆d−1 and Tropical Oriented Matroids

Develin and Sturmfels showed that regular triangulations of ∆n−1 ×∆d−1 can be thought of as tropical polytopes. Tropical oriented matroids were defined by Ardila and Develin, and were conjectured to be in bijection with all subdivisions of ∆n−1 × ∆d−1. In this paper, we show that any triangulation of ∆n−1 × ∆d−1 encodes a tropical oriented matroid. We also suggest a new class of combinatorial o...