2005 International Conference on Analysis of Algorithms
Conrado Martínez (ed.)
DMTCS Conference Volume AD (2005), pp. 173180
author:  Bernhard Gittenberger and Alois Panholzer 

title:  Some results for monotonically labelled simply generated trees 
keywords:  simply generated trees, monotone labellings, node depth, leaf height 
abstract: 
We consider simply generated trees, where the nodes are
equipped with weakly monotone labellings with elements of
{1, 2, …, r}
, for
r
fixed. These tree families were introduced in
[ProUrb1983] and studied further in [Kir1984], [Bli1987],
and [MorPro2005]. Here we give distributional results for
several tree statistics (the depth of a random node, the
ancestortree size and the Steinerdistance 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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reference:  Bernhard Gittenberger and Alois Panholzer (2005), Some results for monotonically labelled simply generated trees, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 173180 
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