The minimal-coefficient formula for Jack superpolynomials

Let $\Lambda$ be a superpartition, let $D[\Lambda]$ be its diagram, and let $a_{\Lambda}(s)$ and $\ell_{\Lambda}(s)$ denote respectively the arm and leg statistics of a cell $s\in D[\Lambda]$. Let $\Lambda^{\circ}$ be the set of cells that do not lie simultaneously in a row containing a circle and a column containing a circle. Write $J_\Lambda^{(1/\beta)}$ for the Jack superpolynomial and $\tilde m_{\Lambda_{\mathrm{min}}}$ for the minimal supermonomial, where $\Lambda_{\mathrm{min}}$ is defined in the source's minimal-partition construction. The minimal-coefficient formula. The coefficient $c_\Lambda^{\mathrm{min}}(\beta)$ of $\tilde m_{\Lambda_{\mathrm{min}}}$ in the monomial expansion of $J_\Lambda^{(1/\beta)}$ is

$$c_\Lambda^{\mathrm{min}}(\beta)=\frac{1}{\prod_{s\in\Lambda^{\circ}}\left(a_\Lambda(s)/\beta+\ell_\Lambda(s)+1\right)}.$$

This formula was inferred from computer experimentation and is presented as a conjecture; its general validity is not established in the supplied text.