The generation conjecture for the supersymmetric polynomial algebra

Let $A_s$ be the algebra of supersymmetric polynomials and let $A_s(p)$ be the subalgebra defined in the paper. Generation conjecture for $A_s$. The algebra $A_s$ is generated over $A_s(p)$ by the elements $c_r$ for $r\geq 0$. The paper states that, together with Proposition 5.1, this conjecture would imply the preceding generation statement for $R_{pol}$; its resolution therefore controls the proposed Donkin–Koppinen filtration.