We first extend the results of CKSV22 by showing that the degree $d$ elementary symmetric polynomials in $n$ variables have formula lower bounds of $\Omega(d(n-d))$ over fields of positive characteristic.
Then, we show that the results of the universality of the symmetric model from Shp02 and the results about border ... more >>>

It is a well-known fact that the permanent polynomial is complete for the complexity class VNP, and it is largely suspected that the determinant does not share this property, despite its similar expression.
We study the question of why the VNP-completeness proof of the permanent fails for the determinant.
We ... more >>>