2 problems

Let $D$ be a doubly stochastic matrix of order $n$, meaning that it has nonnegative real entries and every row and column sums to $1$. Its binary diagonal X-ray is the vector…

A binary diagonal X-ray of an $n \times n$ permutation matrix is its diagonal X-ray with entries in $\{0,1\}$. A tournament is a loopless directed graph in which exactly one of…