On blockers in bounded posets

Antichains of a finite bounded poset are assigned antichains playing a role analogous to that played by blockers in the Boolean lattice of all subsets of a finite set. Some properties of lattices of generalized blockers are discussed.Comment: 9 pages; published versio

Pattern Recognition on Oriented Matroids: Halfspaces, Convex Sets and Tope Committees

The principle of inclusion-exclusion is applied to subsets of maximal covectors contained in halfspaces of a simple oriented matroid and to convex subsets of its ground set for enumerating tope committees.Comment: 15 pages; v.2 - minor improvements, v.3,4 - new Section 7 and references adde