Enumerative combinatorics
Bijection for ternary trees and non-crossing trees
Discrete Mathematics
Bijections for a class of labeled plane trees
European Journal of Combinatorics
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According to the Fibonacci number which is studied by Prodinger et al., we introduce the 2-plane tree which is a planted plane tree with each of its vertices colored with one of two colors and -free. The similarity of the enumeration between 2-plane trees and ternary trees leads us to build several bijections. Especially, we found a bijection between the set of 2-plane trees of n+1 vertices with a black root and the set of ternary trees with n internal vertices. We also give a combinatorial proof for a relation between the set of 2-plane trees of nn