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arXiv · 1712.09507

Protected Vertices in Motzkin trees

Anthony Van Duzer
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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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Anthony Van Duzer. 2017-12-27. Protected Vertices in Motzkin trees. https://arxiv.org/abs/1712.09507

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