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Let $A$ be an $n\times n$ skew-symmetric matrix of rank $r$. Given subsets $X$ and $Y$ of row and column indices respectively, let $A_{X,Y}$ denote the submatrix of $A$ obtained by only keeping rows ...

Question. Is there a closed-form expression for the determinant of a $n \times n$ matrix $A$ with entries $$ A_{i,j} = \frac{1 - \delta_{i, j}}{z_i - z_j}, \qquad 1\leq i, j\leq n, $$ where $z_i$ ...