A rank 18 Waring decomposition of $s{M}_{⟨3⟩}$ with 432 symmetries

Abstract

The recent discovery that the exponent of matrix multiplication is determined by the rank of the symmetrized matrix multiplication tensor has invigorated interest in better understanding symmetrized matrix multiplication. I present an explicit rank 18 Waring decomposition of $s{M}_{⟨3⟩}$ and describe its symmetry group.