Pattern Recognition on Oriented Matroids

5locking Sets of Set Families, and Absolute Blocking Constructions in Posets

Let := [A1, ..., Aα} be a nonempty family of nonempty and pairwise distinct subsets of its finite ground set $\text{V}\left(A\right):={\displaystyle \cup {t-1}_{\alpha }^{}}{A}_t.$ Recall that a subset B ⊆ S of a set S ⊇ V() is called a blocking set of the family if for each index i ∈ [α], we have

$\left|B\cap A_i\right|>0.\left(5.1\right)$

The blocker () of the family is defined to be the family of all inclusion-minimal ...