On Weighted Path Lengths And Distances In Increasing Trees

Authors:
M. Kuba;A. Panholzer
Affiliations:
Institut fü/r Diskrete Mathematik und Geometrie Technische Universitä/t Wien 1040 Wien Austria E-mail: markus.kuba@tuwien.ac.at/ alois.panholzer@tuwien.ac.at;Institut fü/r Diskrete Mathematik und Geometrie Technische Universitä/t Wien 1040 Wien Austria E-mail: markus.kuba@tuwien.ac.at/ alois.panholzer@tuwien.ac.at
Venue:
Probability in the Engineering and Informational Sciences
Year:
2007

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Abstract

We study weighted path lengths (depths) and distances for increasing tree families. For those subclasses of increasing tree families, which can be constructed via an insertion process (e.g., recursive trees, plane-oriented recursive trees, and binary increasing trees), we can determine the limiting distribution that can be characterized as a generalized Dickman's infinitely divisible distribution.