Motzkin树叶点的计数  

Counting leaves in Motzkin trees

作　　者：王灿铖 杨胜良[1] WANG Cancheng;YANG Shengliang(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《纯粹数学与应用数学》2024年第2期357-365,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(11861045)。

摘　　要：本文主要研究了n条边的Motzkin树的叶点总数.分别利用符号化方法和双射证明了n条边的Motzkin树的叶点总数与长度为n的自由的Motzkin路的个数相等.利用这个双射也可以得到n个内点的完全二元树的叶点总数,并且给出了半长为n的且有k个峰的Dyck路的个数是Narayana数这一结论一个新的证明.In this paper, we mainly study the total number of leaves of Motzkin trees with n edges. By using symbolic method and bijection respectively, we prove that the total number of leaves of Motzkin trees with n edges is equal to the number of free Motzkin paths with length n. Using this bijection we also get the total number of leaves of full binary trees with n internal nodes, and give a new proof that the number of Dyck paths with semilength n and k leaves is the Narayana number.

关 键 词：Motzkin树 自由的Motzkin路 符号化方法 Narayana数 

分 类 号：O157[理学—数学]