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

9 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

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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

U2 - 10.1016/j.disc.2017.04.007

DO - 10.1016/j.disc.2017.04.007

M3 - Article

AN - SCOPUS:85019196760

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

Abstract

Keywords

ASJC Scopus subject areas

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