Protected Branches in Ordered Trees  

作　　者：Lin Yang Shengliang Yang 

机构地区：[1]Department of Applied Mathematics,Lanzhou University of Technology,Lanzhou 730050,China

出　　处：《Journal of Mathematical Study》2023年第1期1-17,共17页数学研究（英文）

基　　金：supported by theNational Natural Science Foundation of China(Grant Nos.11861045 and 12101280);Gansu Province Science Foundation for Youths(Grant No.20JR10RA187).

摘　　要：In this paper,we consider the class of ordered trees and its two subclasses,bushes and planted trees,which consist of the ordered trees with root degree at least 2 and with root degree 1 respectively.In these three classes,we study the number of trees of size n with k protected(resp.unprotected)branches,and the total number of branches(resp.protected branches,unprotected branches)among all trees of size n.The explicit formulas as well as the generating functions are obtained.Furthermore,we find that,in each class,as n goes to infinity,the proportion of protected branches among all branches in all trees of size n approaches 1/3.

关 键 词：ordered tree BUSH planted tree protected branch unprotected branch Catalan number generating function 

分 类 号：O17[理学—数学]