2-noncrossing trees and 5-ary trees

Recently, Gu et al. [N.S.S. Gu, N.Y. Li, T. Mansour, 2-Binary trees: Bijections and related issues, Discrete Math. 308 (2008) 1209–1221] introduced 2-binary trees and 2-plane trees which are closely related to ternary trees. In this note, we study the 2-noncrossing tree, a noncrossing tree in which...

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Bibliographic Details
Published in:Discrete mathematics 2009-10, Vol.309 (20), p.6135-6138
Main Authors: Yan, Sherry H.F., Liu, Xuezi
Format: Article
Language:English
Subjects:
2-noncrossing tree
5-ary tree
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
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Summary:Recently, Gu et al. [N.S.S. Gu, N.Y. Li, T. Mansour, 2-Binary trees: Bijections and related issues, Discrete Math. 308 (2008) 1209–1221] introduced 2-binary trees and 2-plane trees which are closely related to ternary trees. In this note, we study the 2-noncrossing tree, a noncrossing tree in which each vertex is colored black or white and there is no ascent ( u , v ) such that both the vertices u and v are colored black. By using the representation of Panholzer and Prodinger for noncrossing trees, we find a correspondence between the set of 2-noncrossing trees of n edges with a black root and the set of 5-ary trees with n internal vertices.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2009.03.044