Geodesic
The number of rooted trees of given depth
Péter Pál Pach1 ; Gabriella Pluhár2 ; András Pongrácz3 ; Csaba Szabó2
1University of Technology and Economics
2Eötvös Loránd University, Budapest
3Central European University
The electronic journal of combinatorics, Tome 20 (2013) no. 2
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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.
DOI : 10.37236/3367
Classification : 05C05, 05C30, 05A15, 05A16
Mots-clés : depth, counting

Péter Pál Pach  1   ; Gabriella Pluhár  2   ; András Pongrácz  3   ; Csaba Szabó  2

1 University of Technology and Economics
2 Eötvös Loránd University, Budapest
3 Central European University 
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     author = {P\'eter P\'al Pach and Gabriella Pluh\'ar and Andr\'as Pongr\'acz and Csaba Szab\'o},
     title = {The number of rooted trees of given depth},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {2},
     doi = {10.37236/3367},
     zbl = {1266.05011},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3367/}
}
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Péter Pál Pach; Gabriella Pluhár; András Pongrácz; Csaba Szabó. The number of rooted trees of given depth. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/3367

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