2 problems

Guillon–Jeandel conjecture. If a $\mathbb{Z}$-subshift induces to a sofic $\mathbb{Z}^2$-subshift, then the original $\mathbb{Z}$-subshift is sofic.

Let $L=\mathbb{Z}_{2}\wr\mathbb{Z}$ be the lamplighter group, and suppose its cogrowth coefficients have asymptotic form … The numerical ratio analysis gives $1/2<\sigma<3/4$. Lamp…