Lengths of paths in rooted trees

2018/06/18 by Keith Copenhaver, Copenhaver, Keith
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.1806.06925

openalex publication_date 2018/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide formulas for generating functions of many types of paths in various rooted tree structures. We compute the kth moment of the generating functions for various types of vertical paths. In two specific familes of trees we find exact closed formulas for expectations and their asymptotic values. Some of these closed formulas are surprisingly simple.

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