  Following a recent publication, in this paper we count the number of
independent operators at arbitrary mass dimension in $N=1$ supersymmetric gauge
theories and derive their field and derivative content. This work uses Hilbert
series machinery and extends a technique from our previous work on handling
integration by parts redundancies to vector superfields. The method proposed
here can be applied to both abelian and non-abelian gauge theories and for any
set of (chiral/antichiral) matter fields. We work through detailed steps for
the abelian case with single flavor chiral superfield at mass dimension eight,
and provide other examples in the appendices.
