Enumeration of Protected nodes in Motzkin trees
Enumeration of Protected nodes in Motzkin trees
Received:December 16, 2019  Revised:December 24, 2020
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中文关键词:  
英文关键词:Motzkin trees  Protected nodes  Motzkin number  Bivariate generating function  Lagrange inversion
基金项目:
Author NameAffiliationE-mail
Lin Yang Lanzhou University of Technology yanglinmath@163.com 
Sheng-Liang Yang Lanzhou University of Technology  
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中文摘要:
      
英文摘要:
      In this paper, we enumerate the set of Motzkin trees with $n$ edges according to the number of protected nodes, the number of protected branch nodes, and the number of protected lonely nodes. Explicit formulas as well as generating functions are obtained. We also find that, as $n$ goes to infinite, 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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