{"paper":{"title":"The hyperdeterminant of 3 x 3 x 2 arrays, and the simplest invariant of 4 x 4 x 2 arrays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Murray R. Bremner","submitted_at":"2011-11-25T22:22:23Z","abstract_excerpt":"We use the representation theory of Lie algebras and computational linear algebra to obtain an explicit formula for the hyperdeterminant of a $3 \\times 3 \\times 2$ array: a homogeneous polynomial of degree 12 in 18 variables with 16749 monomials and 41 distinct integer coefficients; the monomials belong to 178 orbits under the action of $(S_3 \\times S_3 \\times S_2) \\rtimes S_2$. We also obtain the simplest invariant for a $4 \\times 4 \\times 2$ array: a homogeneous polynomial of degree 8 in 32 variables with 14148 monomials and 13 distinct integer coefficients; the monomials belong to 28 orbits"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6120","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"}