{"paper":{"title":"Classification of subspaces in ${\\mathbb{F}}^2\\otimes {\\mathbb{F}}^3$ and orbits in ${\\mathbb{F}}^2\\otimes {\\mathbb{F}}^3\\otimes {\\mathbb{F}}^r$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"John Sheekey, Michel Lavrauw","submitted_at":"2015-03-13T14:00:34Z","abstract_excerpt":"This paper contains the classification of the orbits of elements of the tensor product spaces ${\\mathbb{F}}^2\\otimes {\\mathbb{F}}^3 \\otimes{\\mathbb{F}}^r$, $r\\geq 1$, under the action of two natural groups, for all finite; real; and algebraically closed fields. For each of the orbits we determine: a canonical form; the tensor rank; the rank distribution of the contraction spaces; and a geometric description. The proof is based on the study of the contraction spaces in ${\\mathrm{PG}}({\\mathbb{F}}^2\\otimes{\\mathbb{F}}^3)$ and is geometric in nature. Although the main focus is on finite fields, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07894","kind":"arxiv","version":2},"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"}