Planted Planar Tree

A planted plane tree (V,E,v,alpha) is defined as a vertex set V, edges set E, root v, and order relation alpha on V which satisfies

1. For x,y in V if rho(x)<rho(y), then xalphay, where rho(x) is the length of the path from v to x,

2. If {r,s}, {x,y} in E, rho(r)=rho(x)=rho(s)-1=rho(y)-1 and ralphax, then salphay

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

See also

Catalan Number, Planted Tree, Tree

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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.

Referenced on Wolfram|Alpha

Planted Planar Tree

Cite this as:

Weisstein, Eric W. "Planted Planar Tree." From MathWorld--A Wolfram Web Resource.

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