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The Distribution of Patterns in Random Trees

Frédéric Chyzak·Michael Drmota·Thomas Klausner·Gerard Kok
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Abstract

Let $T\_n$ denote the set of unrooted labeled trees of size $n$ and let $T\_n$ be a particular (finite, unlabeled) tree. Assuming that every tree of $T\_n$ is equally likely, it is shown that the limiting distribution as $n$ goes to infinity of the number of occurrences of $M$ as an induced subtree is asymptotically normal with mean value and variance asymptotically equivalent to $μn$ and $σ^2n$, respectively, where the constants $μ>0$ and $σ\ge 0$ are computable.

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Frédéric Chyzak, Michael Drmota, Thomas Klausner, Gerard Kok. 2006-05-05. The Distribution of Patterns in Random Trees. https://arxiv.org/abs/cs/0605019

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