Levi-Civita张量的稳定性及一个Alon-Tarsi型定理

Pub Date : 2023-10-31 DOI:10.5802/crmath.505

Damir Yeliussizov

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引用次数: 0

摘要

我们证明了几何不变理论意义上的列维-奇维塔张量是半稳定的，这相当于拉丁平方上的阿隆-塔西猜想的一个类似。证明利用了Tao的片秩与半稳定张量的联系。我们也给出了罗塔基猜想的渐近饱和型的一个应用。

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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 saturation-type version of Rota’s basis conjecture.

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