Geodesic
Some results for monotonically labelled simply generated trees
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms (2005).

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We consider simply generated trees, where the nodes are equipped with weakly monotone labellings with elements of $\{1, 2, \ldots, r\}$, for $r$ fixed. These tree families were introduced in Prodinger and Urbanek (1983) and studied further in Kirschenhofer (1984), Blieberger (1987), and Morris and Prodinger (2005). Here we give distributional results for several tree statistics (the depth of a random node, the ancestor-tree size and the Steiner-distance of $p$ randomly chosen nodes, the height of the $j$-st leaf, and the number of nodes with label $l$), which extend the existing results and also contain the corresponding results for unlabelled simply generated trees as the special case $r=1$. 
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     author = {Gittenberger, Bernhard and Panholzer, Alois},
     title = {Some results for monotonically labelled simply generated trees},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms},
     year = {2005},
     doi = {10.46298/dmtcs.3356},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3356/}
}
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Gittenberger, Bernhard; Panholzer, Alois. Some results for monotonically labelled simply generated trees. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms (2005). doi : 10.46298/dmtcs.3356. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3356/

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