3 problems

Let $R(n,k)$ be the matrix introduced in the paper, and let $R^{-1}(n,k)$ denote its inverse matrix. The fifth conjecture. (1) For fixed $k$ and any prime power $p^e$ with…

Let $M(m,n)$ be the excedance matrix, and let $N(m,n)$ be obtained by reversing the order of its rows: its $i$th row is the $(m-i+1)$st row of $M(m,n)$. A matrix is totally nonnega…

Let $T_3^{\le 2}$ denote the specified binary matrix family, and let $\operatorname{sat}(n,F)$ be the minimum number of columns in an $n$-row $F$-saturated matrix. Set…