Pattern Recognition on Oriented Matroids

Blocking Sets of Set Families, and Absolute Blocking Constructions in Posets

Let := {A1,..., Aα} be a nonempty family of nonempty and pairwise distinct subsets of a finite ground set $V\left(A\right):={\cup }_{i-1}^a{A}_i.$ . The family is called a Sperner family (or a clutter) if

$A_i\cancel{\subseteq }{A}_j,$

for all i, j ∈ [a], i ≠ j.

A blocking set of the family is defined to be a subset B ⊆ S of a set S ⊇ V() such that

$\left|B\cap A_i\right|>0,($