| Motzkin树上的保护点的计数问题 |
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| 引用本文： | 杨琳,杨胜良.Motzkin树上的保护点的计数问题[J].数学研究及应用,2021,41(2):127-140. |
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| 作者姓名： | 杨琳 杨胜良 |
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| 作者单位： | 兰州理工大学理学院, 甘肃 兰州 730050 |
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| 基金项目： | 国家自然科学基金(Grant No.11861045), 甘肃省青年基金(Grant No.20JR10RA187), 兰州理工大学红柳一级学科基金. |
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| 摘 要： | In this paper,we enumerate the set of Motzkin trees with n edges according to the number of leaves,the number of vertices adjacent to a leaf,the number of protected nodes,the number of(protected)branch nodes,and the number of(protected)lonely nodes.Explicit formulae as well as generating functions are obtained.We also find that,as n goes to infinity,the proportion of protected branch nodes and protected lonely nodes among all vertices of Motzkin trees with n edges approaches 4/27 and 2/9.
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| 关 键 词： | Motzkin trees protected nodes Motzkin number Bivariate generating function Lagrange inversion |
| 收稿时间： | 2019/12/16 0:00:00 |
| 修稿时间： | 2021/1/3 0:00:00 |
Enumeration of Protected Nodes in Motzkin Trees |
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| Lin YANG,Shengliang YANG.Enumeration of Protected Nodes in Motzkin Trees[J].Journal of Mathematical Research with Applications,2021,41(2):127-140. |
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| Authors: | Lin YANG Shengliang YANG |
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| Institution: | School of Science, Lanzhou University of Technology, Gansu 730050, P. R. China |
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| Abstract: | In this paper, we enumerate the set of Motzkin trees with $n$ edges according to the number of leaves, the number of vertices adjacent to a leaf, the number of protected nodes, the number of (protected) branch nodes, and the number of (protected) lonely nodes. Explicit formulae as well as generating functions are obtained. We also find that, as $n$ goes to infinity, the proportion of protected branch nodes and protected lonely nodes among all vertices of Motzkin trees with $n$ edges approaches $4/27$ and $2/9$. |
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| Keywords: | Motzkin trees protected nodes Motzkin number Bivariate generating function Lagrange inversion |
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