Planted Planar Tree

A planted plane tree  is defined as a vertex set , edges set , root , and order relation  on  which satisfies

1. For  if , then , where  is the length of the path from  to ,

2. If , ,  and , then 

(Klarner 1969, Chorneyko and Mohanty 1975). The Catalan numbers give the number of planar trivalent planted trees.

REFERENCES

Chorneyko, I. Z. and Mohanty, S. G. "On the Enumeration of Certain Sets of Planted Plane Trees." J. Combin. Th. Ser. B 18, 209-221, 1975.

Harary, F.; Prins, G.; and Tutte, W. T. "The Number of Plane Trees." Indag. Math. 26, 319-327, 1964.

Klarner, D. A. "A Correspondence Between Sets of Trees." Indag. Math. 31, 292-296, 1969.