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 [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text] are non-negative 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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