Central limit theorem for the bifurcation ratio of a random binary tree
Central limit theorem for the bifurcation ratio of a random binary tree
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随机二叉树分叉比的中心极限定理
DOI：
10.1088/1751-8113/42/41/415002
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Y. Yamazaki
中科院分区：
文献类型：
--
作者：
Ken Yamamoto;Y. Yamazaki
In order to formulate and examine the central limit theorem for a binary tree numerically, a method for generating random binary trees is presented. We first propose the correspondence between binary trees and a certain type of binary sequences (which we call Dyck sequences). Then, the method for generating random Dyck sequences is shown. Also, we propose the method of branch ordering of a binary tree by means of only the corresponding Dyck sequence. We confirm that the method is in good consistency with the topological analysis of binary trees known as the Horton–Strahler analysis. Two types of central limit theorem are numerically confirmed, and the obtained results are expressed in simple forms. Furthermore, the proposed method is available for a wide range of the topological analysis of binary trees.
