Trying to build a reduction from the maximum coverage problem to my research problem, I'm facing this difficulty :
Let $X$ be a $n \times m$ binary matrix (with $m > n$), can we define a square matrix $M = \begin{bmatrix} A & X\\ X^\top & B \end{bmatrix}$ such that $\det M$ is related to the number of non zero columns of $X$ ?
All my attempts failed, but perhaps I was looking in a wrong direction...