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arXiv · 1403.2928

An arborist's guide to the rationals

Katherine E. Stange
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Abstract

There are two well-known ways to enumerate the positive rational numbers in an infinite binary tree: the Farey/Stern-Brocot tree and the Calkin-Wilf tree. In this brief note, we describe these two trees as `transpose shadows' of a tree of matrices (a result due to Backhouse and Ferreira) via a new proof using yet another famous tree of rationals: the topograph of Conway and Fung.

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Katherine E. Stange. 2014-03-21. An arborist's guide to the rationals. https://arxiv.org/abs/1403.2928

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