Abstract
We give new interpretations of Catalan and convoluted Catalan numbers in terms of trees and chain blockers. For a poset P we say that a subset A ⊆ P is a chain blocker if it is an inclusionwise minimal subset of P that contains at least one element from every maximal chain. In particular, we study the set of chain blockers for the class of posets P = C a × C b where C i is the chain 1 < ⋯ < i. We show that subclasses of these chain blockers are counted by Catalan and convoluted Catalan numbers.
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