The Pieri formulas conjecture for Schur superpolynomials

Let $s_\Lambda$ be a Schur superpolynomial indexed by a superpartition, and let $(;r)$, $(r;)$, $(;1^r)$ and $(0;1^r)$ denote the corresponding bosonic and fermionic row and column superpartitions. For a resulting diagram $\Omega$, let $\#\ell_\odot$ be the number of circles in $\Omega$ lying below the newly added circle. Pieri formulas conjecture.

$$s_\Lambda s_{(;r)}=\sum_{\Omega\in\Lambda\otimes(;r)}s_\Omega,\qquad s_\Lambda s_{(r;)}=\sum_{\Omega\in\Lambda\otimes(r;)}(-1)^{\#\ell_\odot}s_\Omega,$$

and

$$s_\Lambda s_{(;1^r)}=\sum_{\Omega\in\Lambda\otimes(;1^r)}s_\Omega,\qquad s_\Lambda s_{(0;1^r)}=\sum_{\Omega\in\Lambda\otimes(0;1^r)}(-1)^{\#\ell_\odot}s_\Omega.$$

These formulas conjecturally describe multiplication by elementary row and column Schur superpolynomials through admissible Pieri diagrams, with signs controlled by fermionic circles; the source gives no resolution status.