Product Ranks of the $3imes 3$ Determinant and Permanent

Canadian mathematical bulletin

Nathan Ilten²  Zach Teitler¹ 

[1] Department of Mathematics, Boise State University, 1910 University Drive Boise, ID 83725-1555, USA;Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby BC V5A1S6

关键词: product rank;    tensor rank;    determinant;    permanent;    Fano schemes;   

DOI  :  10.4153/CMB-2015-076-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We show that the product rank of the $3 imes 3$ determinant$det_3$ is $5$,and the product rank of the $3 imes 3$ permanent$operatorname{perm}_3$is $4$.As a corollary, we obtain that the tensor rank of $det_3$ is$5$ and the tensor rank of $operatorname{perm}_3$ is $4$.We show moreover that the border product rank of $operatorname{perm}_n$ islarger than $n$ for any $ngeq 3$.

【 授权许可】

Unknown