Enumerations of vertices among all rooted ordered trees with levels and degrees

Sen Peng Eu; Seunghyun Seo; Heesung Shin

doi:10.1016/j.disc.2017.04.007

Enumerations of vertices among all rooted ordered trees with levels and degrees

Sen Peng Eu, Seunghyun Seo, Heesung Shin^*

^*Corresponding author for this work

Department of Mathematics

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

6 Citations (Scopus)

Abstract

In this paper we enumerate and give bijections for the following four sets of vertices among rooted ordered trees of a fixed size: (i) first-children of degree k at level ℓ, (ii) non-first-children of degree k at level ℓ−1, (iii) leaves having k−1 elder siblings at level ℓ, and (iv) non-leaves of outdegree k at level ℓ−1. Our results unite and generalize several previous works in the literature.

Original language	English
Pages (from-to)	2123-2129
Number of pages	7
Journal	Discrete Mathematics
Volume	340
Issue number	9
DOIs	https://doi.org/10.1016/j.disc.2017.04.007
Publication status	Published - 2017 Sept 1

Keywords

Degree
Enumeration
Level
Rooted ordered tree

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2017.04.007

Cite this

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abstract = "In this paper we enumerate and give bijections for the following four sets of vertices among rooted ordered trees of a fixed size: (i) first-children of degree k at level ℓ, (ii) non-first-children of degree k at level ℓ−1, (iii) leaves having k−1 elder siblings at level ℓ, and (iv) non-leaves of outdegree k at level ℓ−1. Our results unite and generalize several previous works in the literature.",

keywords = "Degree, Enumeration, Level, Rooted ordered tree",

author = "Eu, {Sen Peng} and Seunghyun Seo and Heesung Shin",

note = "Funding Information: For the first author, this research was partially supported by Ministry of Science of Technology, Taiwan ROC under grants 104-2115-M-003-014-MY3. For the second author, this study has been worked with the support of a research grant of Kangwon National University in 2015. For the third author, this work was supported by Inha University Research Grant. Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

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doi = "10.1016/j.disc.2017.04.007",

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AU - Eu, Sen Peng

AU - Seo, Seunghyun

AU - Shin, Heesung

N1 - Funding Information: For the first author, this research was partially supported by Ministry of Science of Technology, Taiwan ROC under grants 104-2115-M-003-014-MY3. For the second author, this study has been worked with the support of a research grant of Kangwon National University in 2015. For the third author, this work was supported by Inha University Research Grant. Publisher Copyright: © 2017 Elsevier B.V.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - In this paper we enumerate and give bijections for the following four sets of vertices among rooted ordered trees of a fixed size: (i) first-children of degree k at level ℓ, (ii) non-first-children of degree k at level ℓ−1, (iii) leaves having k−1 elder siblings at level ℓ, and (iv) non-leaves of outdegree k at level ℓ−1. Our results unite and generalize several previous works in the literature.

AB - In this paper we enumerate and give bijections for the following four sets of vertices among rooted ordered trees of a fixed size: (i) first-children of degree k at level ℓ, (ii) non-first-children of degree k at level ℓ−1, (iii) leaves having k−1 elder siblings at level ℓ, and (iv) non-leaves of outdegree k at level ℓ−1. Our results unite and generalize several previous works in the literature.

KW - Degree

KW - Enumeration

KW - Level

KW - Rooted ordered tree

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DO - 10.1016/j.disc.2017.04.007

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JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

Enumerations of vertices among all rooted ordered trees with levels and degrees

Abstract

Keywords

ASJC Scopus subject areas

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