7 problems

Binary-matrix finiteness conjecture. Every pair of binary matrices has the finiteness property.

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 $F(0,2^{t-2}+1,1,0)$…

Ordered matrix removal conjecture. For every $k\times k$ binary matrix $A$ and every $\varepsilon>0$, there is a $\delta=\delta(k,\varepsilon)=\operatorname{poly}(\varepsilon)>0$ s…

Gyárfás' conjecture. Every $0$-$1$ matrix $M$ of size $n\times n$ contains a homogeneous staircase of size at least $n-1$, equivalently, if $st(M)$ is the maximum size of a homogen…

A binary matrix is a matrix whose entries belong to $\{0,1\}$. For a finite matrix family, the finiteness property means that some finite product attains the joint spectral radius.…

Let $\mathcal{S}$ be the set of symmetric binary matrices with no row sum greater than one. For $s\in\mathcal{S}$, let $A(s)$ be the set of upper-triangular positions containing a…

Let $\mathcal{A}_N$ be the set of symmetric binary $N\times N$ matrices with no row sum greater than one. For $a=(a_{i,j})$, define … Let $S_{N,i}$ be the coefficient of $Q^i$ in t…