Characterizations of the convex geometries arising from the double shellings of posets

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.