The q-Calkin-Wilf tree

  • Authors:

  • Bruce Bates;Toufik Mansour

  • Affiliations:

  • Centre for Pure Mathematics, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia 2522;Department of Mathematics, University of Haifa, 31905 Haifa, Israel

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

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.