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The height of random binary unlabelled trees

Nicolas Broutin 1 Philippe Flajolet 1
1 ALGORITHMS - Algorithms
Inria Paris-Rocquencourt
Abstract : This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a central and local sense. Moderate as well as large deviations estimates are also derived. The proofs rely on the analysis (in the complex plane) of generating functions associated with trees of bounded height.
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Nicolas Broutin, Philippe Flajolet. The height of random binary unlabelled trees. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. pp.121-134. ⟨hal-01194678⟩

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