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On the tensor rank of $3\times 3$ permanent and determinant

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arxiv 1801.00496 v1 pith:NQERMDOM submitted 2018-01-01 math.CO cs.CC

Siddharth Krishna , Visu Makam This is my paper · ORCID
classification math.COcs.CC
keywords timesdeterminantranktensorpermanenttensorscharacteristicwell
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abstract

The tensor rank and border rank of the $3 \times 3$ determinant tensor is known to be $5$ if characteristic is not two. In this paper, we show that the tensor rank remains $5$ for fields of characteristic two as well. We also include an analysis of $5 \times 5$ and $7 \times 7$ determinant and permanent tensors, as well as the symmetric $3 \times 3$ permanent and determinant tensors. We end with some remarks on binary tensors.

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  1. A bound for the Waring rank of the determinant via syzygies

    math.AG 2019-08 conditional novelty 6.0 of 10

    The 3x3 determinant has Waring rank at least 15, improving the known lower bound from 14, and the cactus rank of the 3x3 permanent is at least 14.

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