9 problems

A vertex-ordered forest is a forest whose vertices carry a linear order; its extremal function is the maximum number of vertices or edges avoiding a fixed ordered forest, and the i…

Let $\rho_n$ denote the maximal determinant of an $n\times n$ $0/1$-matrix. Maximal determinant conjecture. For $n=14$, … At the time of the source, the exact value was reported as…

Singular 0/1-matrix conjecture. The probability that a random square $d$-dimensional $0/1$-matrix is singular satisfies

Let $m$ and $\ell$ be integers with $0<\ell<2m+1$. Consider 0-1 matrices having exactly $m^2+\ell$ ones, and let their spectral radius be maximized over all matrix sizes. Friedland…

Let $F$ be a simple $k\times \ell$ $(0,1)$-matrix. A product of matrices is obtained by stacking, in order, one column from each factor; the factors here are identity matrices $I$,…

Let $\alpha(k,n)$ denote the minimum number of entries equal to $1$ in an $n\times n$ matrix with entries $0$ and $1$ such that every $k\times k$ minor contains at least one entry…

Let $n\geq 3$ and let $A\in\{0,1\}^{n\times n}$ be a nonsingular symmetric 0–1 matrix. The enhanced principal rank characteristic sequence of a symmetric matrix records, for each o…

Let $P$ be a tuple permutation matrix, and let $ex(n,P)$ denote the maximum number of nonzero entries in an $n\times n$ zero-one matrix that avoids $P$. Keszegh's conjecture. … Thi…

Maximal-determinant conjecture. Maximal determinants of 0/1-matrices are attained by 0/1-matrices that represent acute 0/1-simplices.