A combinatorial approach to the analysis of bucket recursive trees

Authors:
Markus Kuba;Alois Panholzer
Affiliations:
Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria;Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria
Venue:
Theoretical Computer Science
Year:
2010

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Abstract

In this work we provide a combinatorial analysis of bucket recursive trees, which have been introduced previously as a natural generalization of the growth model of recursive trees. Our analysis is based on the description of bucket recursive trees as a special instance of the so-called bucket increasing trees, which is a family of combinatorial objects introduced in this paper. Using this combinatorial description we obtain exact and limiting distribution results for the parameter depth of a specified element, descendants of a specified element and degree of a specified element.