@article{76d107ac8245469b9e2b905b43438be6,
title = "Enumerations of vertices among all rooted ordered trees with levels and degrees",
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.",
year = "2017",
month = sep,
day = "1",
doi = "10.1016/j.disc.2017.04.007",
language = "English",
volume = "340",
pages = "2123--2129",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "9",
}