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arXiv · 2503.12032

Recursive Koszul flattenings of determinant and permanent tensors

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

We investigate new lower bounds on the tensor rank of the determinant and the permanent tensors via recursive usage of the Koszul flattening method introduced by Landsberg-Ottaviani and Hauenstein-Oeding-Ottaviani-Sommese. Our lower bounds on $\mathbf{R} (\det_n)$ completely separate the determinant and the permanent tensors by their tensor ranks. Furthermore, we determine the exact tensor ranks $\mathbf{R} (\det_4) = 12$ and $\mathbf{R} (\operatorname{perm}_4) = 8$ over arbitrary field of characteristic $\neq 2$.

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Jong In Han, Jeong-Hoon Ju, Yeongrak Kim. 2025-03-15. Recursive Koszul flattenings of determinant and permanent tensors. https://arxiv.org/abs/2503.12032

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