  Kim and Drake used generating functions to prove that the number of 2-distant
noncrossing matchings, which are in bijection with little Schroeder paths, is
the same as the weight of Dyck paths in which downsteps from even height have
weight 2. This work presents bijections from those Dyck paths to little
Schroeder paths, and from a similar set of Dyck paths to big Schroeder paths.
We show the effect of these bijections on the corresponding matchings, find
generating functions for two new classes of lattice paths, and demonstrate a
relationship with 231-avoiding permutations.
