Linking the Calkin-Wilf and Stern-Brocot trees

Authors

Bruce Bates, University of WollongongFollow
Martin Bunder, University of WollongongFollow
Keith Tognetti, University of WollongongFollow

RIS ID

33113

Publication Details

Bates, B., Bunder, M. & Tognetti, K. (2010). Linking the Calkin-Wilf and Stern-Brocot trees. European Journal of Combinatorics, 31 (7), 1637-1661.

Abstract

Links between the Calkin-Wilif tree and the Stern-Brocot tree are discussed answering the questions: What is the jth vertex in the nth level of 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.