4 problems

Existence conjecture. There is a colouring rule that is stationarily essential.

Let $X=\{0,1\}^{{\mathbf Z}_2*{\mathbf Z}_3}$ carry its canonical measure-preserving action of ${\mathbf Z}_2*{\mathbf Z}_3$. A colouring rule is stationarily essential when no sta…

The paper considers a non-amenable discrete group and a system of equations having the stated normality property. Group-system conjecture. Every such group admits a system of equat…

Let $A$) and $B$ be two $(0,1)$-matrices in $\mathcal M_{n\times \ell}$, with rows $A_i$ and $B_i$, such that … has strictly positive entries. The homogeneous system $(B-A)X=0$ is…