Pattern Recognition on Oriented Matroids

6Committees of Set Families, and Relative Blocking Constructions in Posets

Let r be a rational number, 0 ≤ r < 1. Given a nonempty family := {A1, ..., Aα} of nonempty and pairwise distinct subsets of its finite ground set $V\left(A\right):={\displaystyle {\cup }_{i-1}^{\alpha }{A}_i},$ an r-committee of is defined to be a subset B ⊆ S of a set S ⊇ V() such that

$\left|B\cap A_i\right|>r\cdot \left|B\right|,\left(6.1\right)$

for each i ∈ [α]. Thus, a 0-committee of is nothing else ...