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^*

^*此作品的通信作者

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

9 引文斯高帕斯（Scopus）

摘要

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.

原文	英語
頁（從 - 到）	2123-2129
頁數	7
期刊	Discrete Mathematics
卷	340
發行號	9
DOIs	https://doi.org/10.1016/j.disc.2017.04.007
出版狀態	已發佈 - 2017 9月 1

ASJC Scopus subject areas

理論電腦科學
離散數學和組合

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10.1016/j.disc.2017.04.007

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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.",

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AU - Eu, Sen Peng

AU - Seo, Seunghyun

AU - Shin, Heesung

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

UR - https://www.scopus.com/pages/publications/85019196760

UR - https://www.scopus.com/pages/publications/85019196760#tab=citedBy

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DO - 10.1016/j.disc.2017.04.007

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SN - 0012-365X

VL - 340

SP - 2123

EP - 2129

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 9

ER -

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

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ASJC Scopus subject areas

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