A shadow Markov equation
We introduce an analogue of the classical Markov equation that involves dual numbers $a+\alpha \varepsilon $ with $\varepsilon ^2=0$. This equation characterizes the “shadow Markov numbers” recently considered by one of us. We show that this equation is characterized by invariance by cluster algebra...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.496/ |
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| author | Bonin, Nathan Ovsienko, Valentin |
| author_facet | Bonin, Nathan Ovsienko, Valentin |
| author_sort | Bonin, Nathan |
| collection | DOAJ |
| description | We introduce an analogue of the classical Markov equation that involves dual numbers $a+\alpha \varepsilon $ with $\varepsilon ^2=0$. This equation characterizes the “shadow Markov numbers” recently considered by one of us. We show that this equation is characterized by invariance by cluster algebra mutations. |
| format | Article |
| id | doaj-art-809d54dd228b4d56a1bc90bf4afeef65 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-809d54dd228b4d56a1bc90bf4afeef652025-02-07T11:10:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G91483148910.5802/crmath.49610.5802/crmath.496A shadow Markov equationBonin, Nathan0Ovsienko, Valentin1Laboratoire de Mathématiques de Reims, UMR9008 CNRS, Université de Reims Champagne-Ardenne, U.F.R. Sciences Exactes et Naturelles, Moulin de la Housse - BP 1039, 51687 Reims cedex 2, FranceLaboratoire de Mathématiques de Reims, UMR9008 CNRS, Université de Reims Champagne-Ardenne, U.F.R. Sciences Exactes et Naturelles, Moulin de la Housse - BP 1039, 51687 Reims cedex 2, FranceWe introduce an analogue of the classical Markov equation that involves dual numbers $a+\alpha \varepsilon $ with $\varepsilon ^2=0$. This equation characterizes the “shadow Markov numbers” recently considered by one of us. We show that this equation is characterized by invariance by cluster algebra mutations.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.496/ |
| spellingShingle | Bonin, Nathan Ovsienko, Valentin A shadow Markov equation Comptes Rendus. Mathématique |
| title | A shadow Markov equation |
| title_full | A shadow Markov equation |
| title_fullStr | A shadow Markov equation |
| title_full_unstemmed | A shadow Markov equation |
| title_short | A shadow Markov equation |
| title_sort | shadow markov equation |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.496/ |
| work_keys_str_mv | AT boninnathan ashadowmarkovequation AT ovsienkovalentin ashadowmarkovequation AT boninnathan shadowmarkovequation AT ovsienkovalentin shadowmarkovequation |