  Two subclasses of Motzkin paths, S-Motzkin and T-Motzkin paths, are
introduced. We provide bijections between S-Motzkin paths and ternary trees,
S-Motzkin paths and non-crossing trees, and T-Motzkin paths and ordered pairs
of ternary trees. Symbolic equations for both paths, and thus generating
functions for the paths, are provided. Using these, various parameters
involving the two paths are analyzed.
