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1 claim from 1 paper

1. Mathematics › Tensor decomposition and applications

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

   Ilten and Zach · arXiv (Cornell University) · 2015

   The paper determines the product rank and tensor rank of the 3×3 determinant and permanent, and shows the border product rank of the n×n permanent exceeds n for every n of at least 3.

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   1. UncheckedThe paper shows the 3×3 determinant has product rank 5 and the 3×3 permanent has product rank 4, which gives the same values as their tensor ranks.“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.”