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arXiv · 2102.02777

Recursive Prime Factorizations: Dyck Words as Numbers

Ralph L. Childress
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Abstract

I propose a class of non-positional numeral systems where numbers are represented by Dyck words, with the systems arising from a recursive extension of prime factorization. After describing two proper subsets of the Dyck language capable of uniquely representing all natural numbers and a superset of the rational numbers respectively, I consider "Dyck-complete" languages, in which every member of the Dyck language represents a number. I conclude by suggesting possible research directions.

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Ralph L. Childress. 2021-02-04. Recursive Prime Factorizations: Dyck Words as Numbers. https://arxiv.org/abs/2102.02777

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