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

2011/12/01 by Murray R. Bremner, Bremner, Murray R., Stavros Georgios Stavrou +2
Computer Science · Mathematics · #15A21 #15A69 (Primary) (Secondary) 15-04 #15B33 #20B25 #Advanced Optimization Algorithms Research #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Matrix Theory and Algorithms #Tensor decomposition and applications #math.CO #math.GR #msc:15-04 #msc:15A21 #msc:15A69 #msc:15B33 #msc:20B25

paper · pdf · doi:10.48550/arxiv.1112.0298

11 pages

arxiv created 2011/12/01 · openalex publication_date 2011/12/01 · arxiv updated 2011/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Tensor Decompositions and Applications

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