ON NODE ENUMERATION AND NODE PATH-LENGTH OF ORDERED TREES

Considering the class GAMMA(n, m) of ordered trees with m leaves and n-m internal nodes, a set of generating functions are established for the following problems: (1) the total number nodes with degree r over GAMMA(n, m), (2) the total. path length of nodes over GAMMA(n, m), and (3) the total number of nodes over GAMMA(n, m) on level k. Some particular counting fomulas are derived from them.