Product Ranks of the 3 × 3 Determinant and Permanent

Ilten, Nathan ; Teitler, Zach

Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 311-319

Résumé

We show that the product rank of the $3\,\times \,3$ determinant ${{\det }_{3}}$ is $5$ , and the product rank of the $3\,\times \,3$ permanent $\text{per}{{\text{m}}_{3}}$ is $4$ . As a corollary, we obtain that the tensor rank of ${{\det }_{3}}$ is $5$ and the tensor rank of $\text{per}{{\text{m}}_{3}}$ is $4$ . We show moreover that the border product rank of $\text{per}{{\text{m}}_{3}}$ is larger than $n$ for any $n\,\ge \,3$ .

Détail

DOI : 10.4153/CMB-2015-076-1

Mots-clés : 15A21, 15A69, 14M12, 14N15, product rank, tensor rank, determinant, permanent, Fano schemes

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