The (u,v)-Calkin-Wilf Forest
Sandie Han, Ariane M. Masuda, Satyanand Singh, and Johann Thiel

TL;DR
This paper extends the Calkin-Wilf tree by exploring properties of a generalized (u,v)-Calkin-Wilf forest associated with specific matrices, revealing new symmetry and structural insights into rational number enumeration.
Contribution
It introduces a generalized (u,v)-Calkin-Wilf forest, extending known properties of the original tree to a broader setting involving matrices with nonnegative integer parameters.
Findings
Extended symmetry and successor formulas to the (u,v)-Calkin-Wilf forest
Analyzed the ancestry of rational numbers within the generalized trees
Connected the structure of these trees to matrix representations
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 and , where and 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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