## 5.8The (X, k)-Blocker Map

In this section we consider a family of maps on the antichains of a finite bounded poset that generalize the set-theoretic blocker map on clutters, as well as the poset-theoretic blocker map on antichains, defined by eq. (5.11).

Let X ⊆ Pa be a subset of the set of atoms of a finite bounded poset P, and k a nonnegative integer, k ≤ |Pa|.

Definition 5.29.

if the antichain A is nontrivial, and

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