The generalized Macdonald superpolynomial conjugation conjecture

Let $\Lambda$ and $\Lambda^{\boxcircle}$ be superpartitions such that $\Lambda^{\boxcircle}$ is obtained from $\Lambda$ by replacing a circle by a box. Let $\#(\Lambda,\Lambda^{\boxcircle})$ be the number of circles lying above the row in which that replacement occurs. Define the normalized modified Macdonald superpolynomial by

$$\widehat H_\Lambda=v_\Lambda H_\Lambda,$$

where

$$v_\Lambda=\prod_{s\in\Lambda/\mathcal B\Lambda}\left(1-q^{a_{\Lambda^{\circledast}}(s)}t^{l_{\Lambda^*}(s)+1}\right).$$

Let $\psi$ be the linear map given by

$$\psi(s_\Lambda)=\sum_{\Omega\,|\,\Omega=\Lambda^{\boxcircle}}(-1)^{\#(\Lambda,\Omega)}s_\Omega.$$

Generalized conjugation conjecture. Then

$$\psi(\widehat H_\Lambda)=\sum_{\Omega\,|\,\Omega=\Lambda^{\boxcircle}}(-1)^{\#(\Lambda,\Omega)}\widehat H_\Omega.$$

The claim generalizes the fermionic-degree-one relation to arbitrary fermionic degree, where the resulting superpartition is not unique. The supplied text gives no resolution status.