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Protected Vertices in Motzkin trees

2017/12/27 by Anthony Van Duzer, Van Duzer, Anthony
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1712.09507

openalex publication_date 2017/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we find recurrence relations for the asymptotic probability a vertex is k protected in all Motzkin trees. We use a similar technique to calculate the probabilities for balanced vertices of rank k. From this we calculate upper and lower bounds for the probability a vertex is balanced and upper and lower bounds for the expected rank of balanced vertices.

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