Recursive Prime Factorizations: Dyck Words as Numbers
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866911451080294400 |
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| author | Childress, Ralph L. |
| author_facet | Childress, Ralph L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_02777 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Recursive Prime Factorizations: Dyck Words as Numbers Childress, Ralph L. Formal Languages and Automata Theory Number Theory 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. |
| title | Recursive Prime Factorizations: Dyck Words as Numbers |
| topic | Formal Languages and Automata Theory Number Theory |
| url | https://arxiv.org/abs/2102.02777 |