2-Binary trees: Bijections and related issues

Nancy S.S. Gu; Nelson Y. Li; Toufik Mansour

doi:10.1016/j.disc.2007.04.007

2-Binary trees: Bijections and related issues

Nancy S.S. Gu, Nelson Y. Li, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A 2-binary tree is a binary rooted tree whose root is colored black and the other vertices are either black or white. We present several bijections concerning different types of 2-binary trees as well as other combinatorial structures such as ternary trees, non-crossing trees, Schröder paths, Motzkin paths and Dyck paths. We also obtain a number of enumeration results with respect to certain statistics.

Original language	English
Pages (from-to)	1209-1221
Number of pages	13
Journal	Discrete Mathematics
Volume	308
Issue number	7
DOIs	https://doi.org/10.1016/j.disc.2007.04.007
State	Published - 6 Apr 2008

Keywords

Binary tree
Dyck path
Motzkin path
Non-crossing tree
Schröder path
Ternary tree

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2007.04.007

Cite this

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title = "2-Binary trees: Bijections and related issues",

abstract = "A 2-binary tree is a binary rooted tree whose root is colored black and the other vertices are either black or white. We present several bijections concerning different types of 2-binary trees as well as other combinatorial structures such as ternary trees, non-crossing trees, Schr{\"o}der paths, Motzkin paths and Dyck paths. We also obtain a number of enumeration results with respect to certain statistics.",

keywords = "Binary tree, Dyck path, Motzkin path, Non-crossing tree, Schr{\"o}der path, Ternary tree",

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AU - Mansour, Toufik

PY - 2008/4/6

Y1 - 2008/4/6

N2 - A 2-binary tree is a binary rooted tree whose root is colored black and the other vertices are either black or white. We present several bijections concerning different types of 2-binary trees as well as other combinatorial structures such as ternary trees, non-crossing trees, Schröder paths, Motzkin paths and Dyck paths. We also obtain a number of enumeration results with respect to certain statistics.

AB - A 2-binary tree is a binary rooted tree whose root is colored black and the other vertices are either black or white. We present several bijections concerning different types of 2-binary trees as well as other combinatorial structures such as ternary trees, non-crossing trees, Schröder paths, Motzkin paths and Dyck paths. We also obtain a number of enumeration results with respect to certain statistics.

KW - Binary tree

KW - Dyck path

KW - Motzkin path

KW - Non-crossing tree

KW - Schröder path

KW - Ternary tree

UR - https://www.scopus.com/pages/publications/38149036993

U2 - 10.1016/j.disc.2007.04.007

DO - 10.1016/j.disc.2007.04.007

M3 - Article

AN - SCOPUS:38149036993

SN - 0012-365X

VL - 308

SP - 1209

EP - 1221

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 7

ER -

2-Binary trees: Bijections and related issues

Abstract

Keywords

ASJC Scopus subject areas

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