8 problems

Let $t$ be given, and let ${\mathrm{forb}}(m,F(0,2^{t-2}+1,1,0))$ denote the maximum number of columns in an $m$-rowed binary matrix avoiding the configuration $F(0,2^{t-2}+1,1,0)$…

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 $I$,…

General equality conjecture.

Let $H(m,2)$ and $H_2(m,2)$ denote the two quantities defined in the paper for integers $m\geq 3$. Equality conjecture. … Consequently, the paper's forbidden-configuration function…

A minimal cubic configuration is a minimal configuration associated with the cubic forbidden-configuration problem; a configuration is minimal when deleting any row or column destr…

Let $F$ be a $k\times \ell$ matrix with $F\ne \begin{bmatrix}0\\ 1\end{bmatrix}$. Let $I_k$ be the $k\times k$ identity matrix, $I_k^c$ its (0,1)-complement, and $T_k$ the…

Forbidden Berge hypergraph conjecture for the 4-cycle.

Let $\mathcal{F}$ be a possibly infinite set of systems of induced equations, and let a Boolean function be $\mathcal{F}$-free when it contains no induced solution of any system in…