Journal of the Australian Mathematical Society

Research Article

The enumeration of rooted trees by total height

John Riordana1 and N. J. A. Sloanea2

a1 Rockefeller University

a2 Cornell University

Abstract

The height (as in [3] and [4]) of a point in a rooted tree is the length of the path (that is, the number of lines in the path) from it to the root; the total height of a rooted tree is the sum of the heights of its points. The latter arises naturally in studies of random neural networks made by one of us (N.J.A.S.), where the enumeration of greatest interest is that of trees with all points distinctly labeled.

(Received July 22 1968)