The Distribution of Patterns in Random Trees

Frédéric Chyzak (1) , Michael Drmota (2) , Thomas Klausner (2) , Gerard Kok (3)

1 ALGO - Algorithms
2 Institut für Diskrete Mathematik und Geometrie [Wien]
3 TWA - Delft Institute of Applied Mathematics

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.

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Frédéric Chyzak, Michael Drmota, Thomas Klausner, Gerard Kok. The Distribution of Patterns in Random Trees. 2006. ⟨inria-00001281⟩