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arXiv · 1503.00822

Product Ranks of the $3\times 3$ Determinant and Permanent

Nathan Ilten·Zach Teitler
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Abstract

We show that the product rank of the $3\times 3$ determinant is $5$, and the product rank of the $3\times 3$ permanent is $4$. As a corollary, we obtain that the tensor ranks of the $3 \times 3$ determinant and permanent are $5$ and $4$, respectively. We show moreover that the border product rank of the $n \times n$ permanent is larger than $n$ for any $n\geq 3$.

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Nathan Ilten, Zach Teitler. 2015-03-03. Product Ranks of the $3\times 3$ Determinant and Permanent. https://doi.org/10.4153/cmb-2015-076-1

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