The Distribution of Patterns in Random Trees

Details The Distribution of Patterns in Random Trees The Distribution of Patterns in Random Trees

2006-05-05

arxiv.org/abs/cs/0605019v1

Computer Science

Discrete Mathematics

Scientific paper

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 $\mu n$ and $\sigma^2n$, respectively, where the constants $\mu>0$ and $\sigma\ge 0$ are computable.

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