The Distribution of Patterns in Random Trees
<|reference_start|>The Distribution of Patterns in Random Trees: 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.<|reference_end|>
@article{chyzak2006the,
    title={The Distribution of Patterns in Random Trees},
    author={Fr'ed'eric Chyzak (INRIA Rocquencourt), Michael Drmota, Thomas
  Klausner, Gerard Kok},
    journal={arXiv preprint arXiv:cs/0605019},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0605019},
    primaryClass={cs.DM math.CO}
}