Deepest Nodes in Marked Ordered Trees

Annales Mathematicae Silesianae

article

Helmut Prodinger¹ 

[1]Department of Mathematical Sciences Stellenbosch University 7602 Stellenbosch South Africa

[2]NITheCS ,(National Institute for Theoretical and Computational Sciences) South Africa

关键词: marked ordered trees;    skew Dyck paths;    generating functions;   

DOI  :  10.2478/amsil-2022-0015

学科分类：内科医学

来源: Walter de Gruyter GmbH

【 摘 要 】

A variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees were introduced by E. Deutsch et al. to model skew Dyck paths. We study the number of deepest nodes in such trees. Explicit generating functions are established and the average number of deepest nodes, which approaches53 {5 \over 3} when the number of nodes gets large. This is to be compared to standard ordered trees where the average number of deepest nodes approaches 2.

【 授权许可】

CC BY