  We compute the generalized Lefschetz number of orientation-preserving
self-homeomorphisms of a compact punctured disk, using the fact that homotopy
classes of these homeomorphisms can be identified with braids. This result is
applied to study Nielsen-Thurston canonical homeomorphisms on a punctured disk.
We determine, for a certain class of braids, the rotation number of the
corresponding canonical homeomorphisms on the outer boundary circle. Also,it is
shown that the canonical homeomorphisms corresponding to some braids are
pseudo-Anosov.
