Abstract
We consider random binary trees under the uniform probability model. Such trees have three types of nodes: Nodes of outdegree 0 (the leaves), 1, and 2. We determine the exact distribution of the number of nodes of each type and show that jointly the three types of nodes asymptotically have a trivariate normal distribution. That trivariate normal limit distribution is completely characterized.
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Communicated by Kurt Mehlhorn.
This research has been supported in part by a grant from NSA: Contract Number MDA904-92-H3086.
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Mahmoud, H.M. The joint distribution of the three types of nodes in uniform binary trees. Algorithmica 13, 313–323 (1995). https://doi.org/10.1007/BF01190510
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DOI: https://doi.org/10.1007/BF01190510