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On Some Parameters in Heap Ordered Trees

Published online by Cambridge University Press:  24 September 2004

KATE MORRIS ,
ALOIS PANHOLZER  and
HELMUT PRODINGER
KATE MORRIS
Affiliation:
The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, P. O. Wits, 2050 Johannesburg, South Africa (e-mail: kate@maths.wits.ac.za, helmut@maths.wits.ac.za)
ALOIS PANHOLZER
Affiliation:
Institut für Algebra und Computermathematik, TU Wien, Wiedner Hauptstr. 8–10, 1040 Wien, Austria (e-mail: Alois.Panholzer@tuwien.ac.at)
HELMUT PRODINGER
Affiliation:
The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, P. O. Wits, 2050 Johannesburg, South Africa (e-mail: kate@maths.wits.ac.za, helmut@maths.wits.ac.za)
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Abstract

Heap ordered trees are planted plane trees, labelled in such a way that the labels always increase from the root to a leaf. We study two parameters, assuming that $p$ of the $n$ nodes are selected at random: the size of the ancestor tree of these nodes and the smallest subtree generated by these nodes. We compute expectation, variance, and also the Gaussian limit distribution, the latter as an application of Hwang's quasi-power theorem.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 13 , Issue 4-5 , July 2004 , pp. 677 - 696
Copyright
© 2004 Cambridge University Press

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