Quantizing Pythagorean triples
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918353194450944 |
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| author | Mathevet, Hugo Morier-Genoud, Sophie Ovsienko, Valentin |
| author_facet | Mathevet, Hugo Morier-Genoud, Sophie Ovsienko, Valentin |
| contents | We introduce a $q$-deformation of the Pythagoras equation $a^2 + b^2 = c^2$, which is a polynomial version of it different from the standard one. We construct a polynomial analogue, or ``$q$-analogue'', of every primitive Pythagorean triple. We also construct such analogue for a larger class of Pythagorean triples called standard. Our approach is based on the notion of $q$-deformed rational numbers and the modular group $\mathrm{PSL}(2,\mathbb{Z})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20536 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantizing Pythagorean triples Mathevet, Hugo Morier-Genoud, Sophie Ovsienko, Valentin Combinatorics We introduce a $q$-deformation of the Pythagoras equation $a^2 + b^2 = c^2$, which is a polynomial version of it different from the standard one. We construct a polynomial analogue, or ``$q$-analogue'', of every primitive Pythagorean triple. We also construct such analogue for a larger class of Pythagorean triples called standard. Our approach is based on the notion of $q$-deformed rational numbers and the modular group $\mathrm{PSL}(2,\mathbb{Z})$. |
| title | Quantizing Pythagorean triples |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.20536 |