标记有序树中的最深节点

IF 0.4 Q4 MATHEMATICS

Annales Mathematicae Silesianae Pub Date : 2022-02-11 DOI:10.2478/amsil-2022-0015

H. Prodinger

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引用次数: 0

摘要

摘要研究了有序树的一种变体，其中每个最右边的边都可能被标记或不被标记，如果它不导致端节点的话。这些有标记的有序树是由E.Deutsch等人引入的，用于对偏斜的Dyck路径进行建模。我们研究了这些树中最深节点的数量。建立了显式生成函数，当节点数量变大时，最深节点的平均数量接近53｛5\超过3｝。这将与最深节点的平均数量接近2的标准有序树进行比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Deepest Nodes in Marked Ordered Trees

Abstract 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 approaches 53 {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.

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来源期刊

Annales Mathematicae Silesianae Mathematics-Mathematics (all)

CiteScore

0.60

自引率

25.00%

发文量

审稿时长

27 weeks