2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165695Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length $2n$ and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.9 pages, 5 figures, revised version, to appear in Discrete MathematicsCombinatoricstext