# A One-to-One Correspondence between Natural Numbers and Binary Trees

arXiv: https://arxiv.org/abs/2002.04477 · HTML: https://mlsanity.com/paper/2002.04477/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [Claycode: Stylable and Deformable 2D Scannable Codes](https://mlsanity.com/paper/2505.08666/) (2025)

## Abstract (arXiv)

A characterization is provided for each natural number except one (1) by means of an ordered pair of elements. The first element is a natural number called the type of the natural number characterized, and the second is a natural number called the order of the number characterized within those of its type. A one-to-one correspondence is specified between the set of binary trees such that a) a given node has no child nodes (that is, it is a terminal node), or b) it has exactly two child nodes. Thus, binary trees such that one of their parent nodes has only one child node are excluded from the set considered here.