Planted Planar Tree
المؤلف:
Chorneyko, I. Z. and Mohanty, S. G.
المصدر:
"On the Enumeration of Certain Sets of Planted Plane Trees." J. Combin. Th. Ser. B 18
الجزء والصفحة:
...
22-5-2022
4432
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 ![<span style=]()
{r,s}" src="https://mathworld.wolfram.com/images/equations/PlantedPlanarTree/Inline13.svg" style="height:21px; width:36px" />, ![<span style=]()
{x,y} in E" src="https://mathworld.wolfram.com/images/equations/PlantedPlanarTree/Inline14.svg" style="height:22px; width:71px" />, 
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.
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