On the tensor rank of the 3 x 3 permanent and determinant

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Siddharth Krishna
Visu Makam


The tensor rank and border rank of the $3 \times 3$ determinant tensor are known to be $5$ if the characteristic is not two. In characteristic two, the existing proofs of both the upper and lower bounds fail. In this paper, we show that the tensor rank remains $5$ for fields of characteristic two as well.

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