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Results tagged with oriented-matroids
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user 54838
Hyperplane arrangements, discrete geometry, convex polytopes, and optimization. For more general questions concerning matroids, use the matroid-theory tag.
5
votes
1
answer
212
views
Reconstructing an oriented matroid from its deletion and contraction
Suppose that $\mathcal{M}_1$ and $\mathcal M_2$ are two oriented matroids on the same ground set $E$. Under what conditions on $\mathcal{M}_1$ and $\mathcal{M}_2$ is there an oriented matroid $\mathca …
- 436
3
votes
Accepted
Reconstructing an oriented matroid from its deletion and contraction
Found the answer in a paper by Ziegler & Richter-Gebert, see Theorem 4.1. Basically, they show that if two oriented matroids $\mathcal{M}_1$, $\mathcal{M}_2$ of ranks $r$ and $r-1$ respectively satis …
- 436