Weakly Protected Points in Ordered Trees

被引：2
|
作者：
Yang, Lin [1 ]
Yang, Sheng-Liang [1 ]
机构：
[1] Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Gansu, Peoples R China
来源：
GRAPHS AND COMBINATORICS | 2021年 / 37卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Ordered trees; Complete binary trees; Motzkin trees; Weakly protected points; Bivariate generating function; Lagrange inversion formula;
D O I：
10.1007/s00373-021-02278-w
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we enumerate the set of ordered trees with n edges according to the number of weakly protected points. Explicit formulas as well as generating functions are obtained. We also find that, as n goes to infinity, the proportion of weakly protected points among all vertices of ordered trees with n edges approaches 1/3.
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页码：775 / 788
页数：14
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