On the Recursive Depth of Special Tree Traversal Algorithms

In this paper we are concerned with the analysis of special recursive algorithms for traversing the nodes of a planted plane tree (ordered tree ; planar tree) . Some by now classical results in this area are due to (de Bruijn, Knuth, and Rice, 1972 ; Knuth, 1973 ; Flajolet, 1981 ; Flajolet and Odlyzko, 1982 ; Flajolet, Raoult, and Vuillemin, 1979 ; Kemp, 1979) and others and are summarized in the next few lines : The most important tree structure in computer science is the binary tree . The family , of binary trees fulfills the symbolic equation