An improved upper bound for the Waring rank of the determinant

Abstract

The Waring rank of the generic $d\times d$ determinant is bounded above by $d\cdot d!$. This improves previous upper bounds, which were of the form an exponential times the factorial. Our upper bound comes from an explicit power sum decomposition. We describe some of the symmetries of the decomposition and set-theoretic defining equations for the terms of the decomposition.