Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem
We show that the Levi-Civita tensors are semistable in the sense of Geometric Invariant Theory, which is equivalent to an analogue of the Alon–Tarsi conjecture on Latin squares. The proof uses the connection of Tao’s slice rank with semistable tensors. We also show an application to an asymptotic sa...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.505/ |
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| author | Yeliussizov, Damir |
| author_facet | Yeliussizov, Damir |
| author_sort | Yeliussizov, Damir |
| collection | DOAJ |
| description | We show that the Levi-Civita tensors are semistable in the sense of Geometric Invariant Theory, which is equivalent to an analogue of the Alon–Tarsi conjecture on Latin squares. The proof uses the connection of Tao’s slice rank with semistable tensors. We also show an application to an asymptotic saturation-type version of Rota’s basis conjecture. |
| format | Article |
| id | doaj-art-d1ce0fed13b943f99b967b0c6eb9cc7a |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-d1ce0fed13b943f99b967b0c6eb9cc7a2025-02-07T11:10:23ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-10-01361G81367137310.5802/crmath.50510.5802/crmath.505Stability of the Levi-Civita tensors and an Alon–Tarsi type theoremYeliussizov, Damir0Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan; Kazakh-British Technical University, Almaty, KazakhstanWe show that the Levi-Civita tensors are semistable in the sense of Geometric Invariant Theory, which is equivalent to an analogue of the Alon–Tarsi conjecture on Latin squares. The proof uses the connection of Tao’s slice rank with semistable tensors. We also show an application to an asymptotic saturation-type version of Rota’s basis conjecture.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.505/ |
| spellingShingle | Yeliussizov, Damir Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem Comptes Rendus. Mathématique |
| title | Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem |
| title_full | Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem |
| title_fullStr | Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem |
| title_full_unstemmed | Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem |
| title_short | Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem |
| title_sort | stability of the levi civita tensors and an alon tarsi type theorem |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.505/ |
| work_keys_str_mv | AT yeliussizovdamir stabilityofthelevicivitatensorsandanalontarsitypetheorem |