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arXiv · 1411.1747

The (u,v)-Calkin-Wilf Forest

Sandie Han·Ariane M. Masuda·Satyanand Singh·Johann Thiel
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Abstract

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.

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Sandie Han, Ariane M. Masuda, Satyanand Singh, Johann Thiel. 2014-11-06. The (u,v)-Calkin-Wilf Forest. https://doi.org/10.1142/s1793042116500809

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