### $(0,1)$-matrices, discrepancy and preservers

Let $m$ and $n$ be positive integers, and let $R=({r}_{1},...,{r}_{m})$ and $S=({s}_{1},...,{s}_{n})$ be nonnegative integral vectors. Let $A(R,S)$ be the set of all $m\times n$$(0,1)$-matrices with row sum vector $R$ and column vector...