Motzkin树叶点的计数
Counting leaves in Motzkin trees
王灿铖 1杨胜良1
作者信息
- 1. 兰州理工大学理学院,甘肃兰州 730050
- 折叠
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.
Abstract
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Key words
Motzkin trees/free Motzkin paths/symbolic method/Narayana number引用本文复制引用
出版年
2024
NETL
NSTL
万方数据