4 problems

Let $\operatorname{md}(n)$ denote the maximal determinant attained by an $n\times n$ matrix with entries in $\{-1,1\}$, and define the normalized maximal determinant by … For order…

Let $R_n$ be an $n\times n$ matrix with entries in $\{-1,1\}$. Hadamard's bound gives … and equality can occur only when $n=1$, $2$, or $n\equiv0\pmod 4$. Paley's conjecture. Equal…

Orrick–Solomon's conjecture. The determinant $72\times9^{17}\times2^{36}$ achieves the global maximum among determinants of $37\times37$ sign matrices.

Let $r$ denote the number of runs, and distinguish affinely full-dimensional factorial designs from subset fractional factorial designs. The D-optimal design conjecture. The $D$-op…