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Determinant and permanent of sum of two $n\times n$ permutation matrices can be arbitrarily different. What is the distribution of determinant of sum and difference of two $n\times n$ permutation ...

Consider the all-familiar Vandermonde determinant $V_n(x_1,\dots,x_n)$ of the matrix of $(i,j)$-entries $M_n(i,j)=x_j^{i-1}$ so that $$V_n(x_1,\dots,x_n)=\prod_{1\leq i<j\leq n}(x_j-x_i).$$ Let's ...