{"paper":{"title":"Ranks of 0-1 arrays of size 2 x 2 x 2 and 2 x 2 x 2 x 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Murray R. Bremner, Stavros G. Stavrou","submitted_at":"2011-12-01T20:36:24Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0298","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}