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

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

2011-12-01

arxiv.org/abs/1112.0298v1

Mathematics

Combinatorics

11 pages

Scientific paper

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.

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