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Random Recursive Trees and Preferential Attachment Trees are Random Split Trees

Part of: Combinatorial probability Graph theory

Published online by Cambridge University Press:  21 May 2018

SVANTE JANSON
SVANTE JANSON*
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden (e-mail: [email protected], http://www.math.uu.se/svante-janson)
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Abstract

We consider linear preferential attachment trees, and show that they can be regarded as random split trees in the sense of Devroye (1999), although with infinite potential branching. In particular, this applies to the random recursive tree and the standard preferential attachment tree. An application is given to the sum over all pairs of nodes of the common number of ancestors.

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 05C05: Trees
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 28 , Issue 1 , January 2019 , pp. 81 - 99
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

†

Partly supported by the Knut and Alice Wallenberg Foundation.

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