Linking the Calkin-Wilf and Stern-Brocot trees

Authors:
Bruce Bates;Martin Bunder;Keith Tognetti
Affiliations:
Centre for Pure Mathematics, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia;Centre for Pure Mathematics, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia;Centre for Pure Mathematics, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia
Venue:
European Journal of Combinatorics
Year:
2010

Citing 3
Cited 2

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Abstract

Links between the Calkin-Wilf tree and the Stern-Brocot tree are discussed answering the questions: What is thejth vertex in thenth level of the Calkin-Wilf tree? and Where is the vertexrslocated in the Calkin-Wilf tree? A simple mechanism is described for converting the jth vertex in the nth level of the Calkin-Wilf tree into the jth entry in the nth level of the Stern-Brocot tree. We also provide a simple method for evaluating terms in the Hyperbinary sequence thus answering a challenge raised in Quantum in September 1997. We also examine successors and predecessors in both trees.