On the Chow-rank of the permanent

Abstract

We derive Glynn's formula from Ryser's formula for the permanent. We further establish via an orbital argument that Glynn's formula yields an optimal row-homogeneous Chow-decomposition of the permanent. We introduce a method for upper-bounding the Chow-rank of polynomials. Our method is based upon the Fundamental Theorem of Symmetric Polynomials. Finally we derive a parametric description of rank revealing row-homogeneous Chow-decompositions of the permanent. Our result provides an alternative approach to the parametrization first obtained by Glynn.