Ranks of 0-1 arrays of size 2 x 2 x 2 and 2 x 2 x 2 x 2

Abstract

We use computer algebra to determine the ranks of arrays of size 2 x 2 x 2 and 2 x 2 x 2 x 2 with entries in the set {0, 1} regarded as a field with two elements, as a Boolean algebra, and as non-negative integers. In the field case we also determine the canonical forms of the arrays with respect to the action of the direct product of the general linear groups.

arXiv comment11 pages

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