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Matrix of high rank mod $2$: must it have a large non-singular minor (with disjoint rows and columns)?

Let $A$ be a $2n$-by-$2n$ matrix with entries in $\mathbb{Z}/2\mathbb{Z}$ such that, for every $2n$-by-$2n$ diagonal matrix $D$ with entries in $\mathbb{Z}/2\mathbb{Z}$, the matrix $A+D$ has rank $\...
H A Helfgott's user avatar
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Number of ways to place 4 kings on nxn chessboard

I have a $n\times n$ chessboard and 4 kings inside it. My goal is to count the number of arrangements where some of them are non-attacking or mutually attacking, for example: In the case where the $4$...
Cardstdani's user avatar