We determine defining equations for the set of concise tensors minimal border rank in $${\mathbb {C}}^m{\mathord { \otimes } }{\mathbb {C}}^m$$ when $$m=5$$ and $$1_*$$ -generic $$m=5,6$$ . solve classical problem algebraic complexity theory classifying special case Our proofs utilize two recent developments: 111-equations defined by Buczyńska–Buczyński results Jelisiejew–Šivic on variety commu...

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Let G be a transitive permutation group acting on a finite set E and let P be the stabilizer in G of a point in E. We say that G is primitive rank 3 on E if P is maximal in G and P has exactly three orbits on E. For any subgroup H of G, we denote by 1H the permutation character (or permutation module) over C of G on the cosets G/H. Let H and K be subgroups of G. We say 1H 6 1 G K if 1 G K − 1 G...