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Characterizations of the convex geometries arising from the double shellings of posets. (English) Zbl 1194.52006

Summary: We investigate the class of double-shelling convex geometries. A double-shelling convex geometry is the collection of sets represented as the intersection of an ideal and a filter of a poset. The size of the stem of any rooted circuit of a double-shelling convex geometry is 2. We characterize the double-shelling convex geometries by the conditions that the rooted circuits should fulfill. Moreover, we also characterize the same class in terms of trace-minimal forbidden minors.

MSC:

52A99 General convexity
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