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

Access to Document

10.1016/j.jcta.2010.09.002

Cite this

@article{ca9cb51e3eaf447c99f31631c0d8efc6,

title = "The q-Calkin-Wilf tree",

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.",

keywords = "Calkin-Wilf sequence, Calkin-Wilf tree, Hyperbinary expansion, Q-Analogue",

author = "Bruce Bates and Toufik Mansour",

year = "2011",

month = apr,

doi = "10.1016/j.jcta.2010.09.002",

language = "English",

volume = "118",

pages = "1143--1151",

journal = "Journal of Combinatorial Theory. Series A",

issn = "0097-3165",

publisher = "Academic Press Inc.",

number = "3",

}

TY - JOUR

T1 - The q-Calkin-Wilf tree

AU - Bates, Bruce

AU - Mansour, Toufik

PY - 2011/4

Y1 - 2011/4

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=78751572823&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2010.09.002

DO - 10.1016/j.jcta.2010.09.002

M3 - Article

AN - SCOPUS:78751572823

SN - 0097-3165

VL - 118

SP - 1143

EP - 1151

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

Access to Document

Other files and links

Fingerprint

Cite this