TL;DR
This paper explores trees similar to the Calkin-Wilf tree, reformulating its construction algebraically and applying number theory to analyze possible analogues of such enumeration trees.
Contribution
It introduces an algebraic reformulation of the Calkin-Wilf tree and uses analytic number theory to restrict potential analogues.
Findings
Reformulation of the Calkin-Wilf tree in algebraic terms
Application of analytic number theory to analyze enumeration trees
Restrictions on possible similar trees
Abstract
In this note we discuss trees similar to the Calkin-Wilf tree, a binary tree that enumerates all positive rational numbers in a simple way. The original construction of Calkin and Wilf is reformulated in a more algebraic language, and an elementary application of methods from analytic number theory gives restrictions on possible analogues.
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Taxonomy
Topicssemigroups and automata theory · Mathematical Dynamics and Fractals