All Questions

Let $M\in\{-1,0,+1\}^{n\times n}$ be a matrix of rank $r$. Consider the matrix $f(M)\in\{0,+1\}^{mn\times mn}$ where $0$ in $M$ is replaced by $m\times m$ all $0$ matrix, $+1$ in $M$ is replaced by $m\...

How many $M\in\{0,1\}^{r\times c}$ are there such that each row and each column of $M$ is distinct? How many classes of matrices in $\{0,1\}^{r\times c}$ up to permutation equivalence are there such ...