... Young tableau. The ordering onis by inclusion, and→ is the obvious function. The cardinality n(∅,λ) of the fiber of the electronic journal of combinatorics 8 (2001), #R32 8then there is a covering ... arealization of the rooted tree t as a planar directed graph (with arrows coming out from the root), then the number of ways to attach the labels {0, 1, ,|t|} to the vertices of Tso that the labels ... coverPis the poset of standard Young tableaux; if P is the poset of rooted trees orderedby inclusion, thenP consists of permutations. We discuss several other examples,including the posets of...