The (u,v)-Calkin-Wilf Forest
| Autor: | Han, Sandie, Masuda, Ariane M., Singh, Satyanand, Thiel, Johann |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Int. J. Number Theory 12 (05) (2016) 1311-1328 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S1793042116500809 |
| Popis: | In this paper we consider a refinement, due to Nathanson, of the Calkin-Wilf tree. In particular, we study the properties of such trees associated with the matrices $L_u=\begin{bmatrix} 1 & 0 \\ u & 1\end{bmatrix}$ and $R_v=\begin{bmatrix} 1 & v \\ 0& 1\end{bmatrix}$, where $u$ and $v$ are nonnegative integers. We extend several known results of the original Calkin-Wilf tree, including the symmetry, numerator-denominator, and successor formulas, to this new setting. Additionally, we study the ancestry of a rational number appearing in a generalized Calkin-Wilf tree. Comment: 18 pages |
| Databáze: | arXiv |
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