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Two interesting oriented matroids. (English) Zbl 0852.05033

Two oriented matroids of rank 3 with 14 elements, differing exactly in one base orientation, are constructed. One of them has a disconnected realization space, the other is non-realizable but has no biquadratic final polynomial (which would effectively prove its non-realizability).

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)
52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
14P10 Semialgebraic sets and related spaces
51A25 Algebraization in linear incidence geometry
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