MORE PATTERNS IN TREES: UP AND DOWN, YOUNG AND OLD, ODD AND EVEN

Nachum Dershowitz (Tel Aviv University and Microsoft Research) 
and 
Shmuel Zaks (Technion - Israel Institute of Technology)

We show how to apply our previous general tree-pattern enumeration
formula [DAM 25] and a new extension thereof to some recent
enumerations of distributions of leaves in ordered trees (by Chen,
Deutsch, and Elizalde) and in bicolored ordered trees (Clark, McCanna,
and Szeeeekely), as well as distributions of certain subpaths in Dyck
lattice paths (by Y. Sun).  Patterns are ordered (plane-planted) trees
with special leaves representing arbitrary or non-leaf subtrees and
ellipses to span any number of subtrees.