The conjectural norm formula for Macdonald superpolynomials

Let $P_\Lambda$ be the Macdonald superpolynomial associated with a superpartition $\Lambda$ of fermionic degree $m$, and let $h^\uparrow_\Lambda$ and $h^\downarrow_\Lambda$ be the products over the squares specified in the source. The norm conjecture. The norm of $P_\Lambda$ is

$$\langle\!\langle P_\Lambda|P_\Lambda\rangle\!\rangle_{q,t}=(-1)^{\binom{m}{2}}q^{|\Lambda^a|}\frac{h^\uparrow_\Lambda}{h^\downarrow_\Lambda}.$$

This formula was conjectured in earlier work and is the norm formula for the bilinear scalar product on Macdonald superpolynomials; the paper relates it to a second, sesquilinear scalar product.