Super Markov Numbers and Signed Double Dimer Covers
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917969457577984 |
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| author | Musiker, Gregg |
| author_facet | Musiker, Gregg |
| contents | We provide a superalgebraic analogue of Markov numbers, which are defined as the Grassmann integer solutions to the equation $x^2 + y^2 + z^2 + (xy + yz + xz)ε= 3(1 + ε)xyz$, as well as applications to the Decorated Super Teichmüller spaces associated to the once-punctured torus and certain annuli. We conclude with further directions for study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Super Markov Numbers and Signed Double Dimer Covers Musiker, Gregg Combinatorics Mathematical Physics Geometric Topology Number Theory 13F60, 17A70, 30F60, 11D25, 05C70 We provide a superalgebraic analogue of Markov numbers, which are defined as the Grassmann integer solutions to the equation $x^2 + y^2 + z^2 + (xy + yz + xz)ε= 3(1 + ε)xyz$, as well as applications to the Decorated Super Teichmüller spaces associated to the once-punctured torus and certain annuli. We conclude with further directions for study. |
| title | Super Markov Numbers and Signed Double Dimer Covers |
| topic | Combinatorics Mathematical Physics Geometric Topology Number Theory 13F60, 17A70, 30F60, 11D25, 05C70 |
| url | https://arxiv.org/abs/2503.21872 |