Bernhard Gittenberger ; Alois Panholzer - Some results for monotonically labelled simply generated trees

dmtcs:3356 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms - https://doi.org/10.46298/dmtcs.3356
Some results for monotonically labelled simply generated treesArticle

Authors: Bernhard Gittenberger 1; Alois Panholzer 1

  • 1 Institut für Diskrete Mathematik und Geometrie [Wien]

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 $r=1$.


Volume: DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: node depth,monotone labellings,leaf height,simply generated trees,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]
Funding:
    Source : OpenAIRE Graph
  • Automatic Expansion of Generating Functions; Code: P 16053
  • Analysis of data structures and tree-like structures; Code: P 18009

1 Document citing this article

Consultation statistics

This page has been seen 204 times.
This article's PDF has been downloaded 197 times.