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The q-Calkin-Wilf tree |
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| Authors: | Bruce Bates |
| Affiliation: | a Centre for Pure Mathematics, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia 2522 b Department of Mathematics, University of Haifa, 31905 Haifa, Israel |
| 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 tree Calkin-Wilf sequence Hyperbinary expansion q-Analogue |
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