## 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.