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We fix integers $u,v \geq 1$, and consider an infinite binary tree$\mathcal{T}^{(u,v)}(z)$ with a root node whose value is a positive rationalnumber $z$. For every vertex $a/b$, we label the left child as $a/(ua+b)$ andright child as $(a+vb)/b$. The resulting tree is known as the$(u,v)$-Calkin-Wilf tree. As $z$ runs over $[1/u,v]\cap \mathbb{Q}$, the vertexsets of $\mathcal{T}^{(u,v)}(z)$ form a partition of $\mathbb{Q}^+$. When$u=v=1$, the mean row value converges to $3/2$ as the row depth increases. Ourgoal is to extend this result for any $u,v\geq 1$. We show that, when $z\in[1/u,v]\cap \mathbb{Q}$, the mean row value in $\mathcal{T}^{(u,v)}(z)$converges to a value close to $v+\log 2/u$ uniformly on $z$.

Mean Row Values in $(u,v)$-Calkin-Wilf Trees