English

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

Combinatorics 2018-01-03 v1 Computational Complexity

Abstract

The tensor rank and border rank of the 3×33 \times 3 determinant tensor is known to be 55 if characteristic is not two. In this paper, we show that the tensor rank remains 55 for fields of characteristic two as well. We also include an analysis of 5×55 \times 5 and 7×77 \times 7 determinant and permanent tensors, as well as the symmetric 3×33 \times 3 permanent and determinant tensors. We end with some remarks on binary tensors.

Keywords

Cite

@article{arxiv.1801.00496,
  title  = {On the tensor rank of $3\times 3$ permanent and determinant},
  author = {Siddharth Krishna and Visu Makam},
  journal= {arXiv preprint arXiv:1801.00496},
  year   = {2018}
}