The Number of Rooted Trees of Given Depth

Péter Pál Pach, Gabriella Pluhár, András Pongrácz, Csaba Szabó

Abstract


In this paper it is shown that the logarithm of the number of non-isomorphic rooted trees of depth $k\geq 3$ is asymptotically $\frac{\pi^2}{6}\cdot\frac{n}{\log\log\dots\log n}$, where $\log$ is iterated $k-2$ times in the denominator.


Keywords


tree, depth, counting

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