Comptes Rendus
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Algebra, Combinatorics
Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem
Damir Yeliussizov1, 2
1 Kazakh-British Technical University, Almaty, Kazakhstan
2 Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1367-1373.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.505
Classification: 14L24, 15A72, 13A50, 05E14, 05B15, 05B35

Damir Yeliussizov 1, 2

1 Kazakh-British Technical University, Almaty, Kazakhstan
2 Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Damir Yeliussizov. Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1367-1373. doi : 10.5802/crmath.505. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.505/

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