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arXiv · 2510.11051

The border rank of the $4 \times 4$ determinant tensor is twelve

Jong In Han·Jeong-Hoon Ju·Yeongrak Kim
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Abstract

We show that the border rank of the $4 \times 4$ determinant tensor is at least $12$ over $\mathbb{C}$, using the fixed ideal theorem introduced by Buczy\'nska-Buczy\'nski and the method by Conner-Harper-Landsberg. Together with the known upper bound, this implies that the border rank is exactly $12$.

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Jong In Han, Jeong-Hoon Ju, Yeongrak Kim. 2025-10-13. The border rank of the $4 \times 4$ determinant tensor is twelve. https://arxiv.org/abs/2510.11051

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