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Hyperplane arrangements, discrete geometry, convex polytopes, and optimization. For more general questions concerning matroids, use the matroid-theory tag.

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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 …
Pavel Galashin's user avatar