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Hyperplane arrangements, discrete geometry, convex polytopes, and optimization. For more general questions concerning matroids, use the matroid-theory tag.
4
votes
The lattice of covectors of an oriented matroid
This is an answer to question 1 (not the modified version in the comments to Ben's answer).
If you consider only L(M), you have lost all the information the orientation provides (beyond the bare fa …
5
votes
Accepted
Functionals on oriented matroids
I think the answer to your first question is "yes".
Oriented matroids can be realized topologically, and I am going to use that language. (This means is that I can pretend the oriented matroid is …