The q-Calkin-Wilf tree

Bruce Bates; Toufik Mansour

doi:10.1016/j.jcta.2010.09.002

The q-Calkin-Wilf tree

Bruce Bates
, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We define a q-analogue of the Calkin-Wilf tree and the Calkin-Wilf sequence. We show that the nth term f(n;q) of the q-analogue of the Calkin-Wilf sequence is the generating function for the number of hyperbinary expansions of n according to the number of powers that are used exactly twice. We also present formulae for branches within the q-analogue of the Calkin-Wilf tree and predecessors and successors of terms in the q-analogue of the Calkin-Wilf sequence.

Original language	English
Pages (from-to)	1143-1151
Number of pages	9
Journal	Journal of Combinatorial Theory. Series A
Volume	118
Issue number	3
DOIs	https://doi.org/10.1016/j.jcta.2010.09.002
State	Published - Apr 2011

Keywords

Calkin-Wilf sequence
Calkin-Wilf tree
Hyperbinary expansion
Q-Analogue

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2010.09.002

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AB - We define a q-analogue of the Calkin-Wilf tree and the Calkin-Wilf sequence. We show that the nth term f(n;q) of the q-analogue of the Calkin-Wilf sequence is the generating function for the number of hyperbinary expansions of n according to the number of powers that are used exactly twice. We also present formulae for branches within the q-analogue of the Calkin-Wilf tree and predecessors and successors of terms in the q-analogue of the Calkin-Wilf sequence.

KW - Calkin-Wilf sequence

KW - Calkin-Wilf tree

KW - Hyperbinary expansion

KW - Q-Analogue

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JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 3

ER -

The q-Calkin-Wilf tree

Abstract

Keywords

ASJC Scopus subject areas

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