Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4654367 | European Journal of Combinatorics | 2009 | 17 Pages |
Abstract
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+1n+1 vertices with a black root and the set of ternary trees with nn internal vertices. We also give a combinatorial proof for a relation between the set of 2-plane trees of n+1n+1 vertices and the set of ternary trees with nn internal vertices.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Nancy S.S. Gu, Helmut Prodinger,