10 problems

Moser's discrepancy conjecture. There exist such signs for which $D=1$ when $n$ is odd, and $D\leq 2$ when $n$ is even.

For even $n$, let $\mathcal{D}(n)$ denote the set of square roots of determinants of $n\times n$ Seidel tournament matrices. The preceding argument shows that, assuming the existen…

Let $n$ be a positive integer. For $0\leq i\leq \frac{n+1}{3}$ and $0\leq j\leq \frac{n+1}{3}$, let $\widetilde{\mathcal{P}}_{i,j}(n)$ be the matrix obtained by stacking the inclus…

Asymptotic enumeration conjecture. We have

Optimal discrepancy conjecture. This construction is best possible for every $n\geq9$; that is, every non-diagonal $n\times n$ zero-sum-square-free $\{-1,1\}$-matrix has discrepanc…

Linear discrepancy conjecture. For every $C>0$, there is an integer $N$ such that, whenever $n\geq N$, every non-diagonal $n\times n$ matrix $M$ with entries in $\{-1,1\}$ and

All-odd-orders conjecture. A circulant good matrix exists in every odd order $n$.

Let $A\in\{0,1\}^{n\times n}$ be a matrix with the 2-consecutive ones property, meaning that the ones in each row occur in at most two blocks in some ordering of the columns. 2-con…

Let $A\in\{0,1\}^{n\times n}$ be a $0/1$-matrix with at most $2n$ non-zero entries. Sparse maximal determinant conjecture. Then … The bound is motivated by block-diagonal matrices…

Let an Order-Regular matrix be a binary matrix satisfying the Order-Regularity constraints arising from Policy Iteration on cube acyclic Unique Sink Orientations. For an $n$-column…