5 problems

SRS weak-tiling conjecture. The collection

SRS tile boundary conjecture. For every $\mathbf{x}\in\mathbb{Z}^d$,

Akiyama's finiteness-property conjecture. For every $d\in\mathbb{N}$,

Let $\mathbf{r}=(r_0,\ldots,r_{d-1})\in\operatorname{int}(\mathcal{D}_d)$ with $r_0\ne0$. Weak-tiling conjecture. The collection … is a weak tiling, meaning a weak $1$-tiling: ever…

Let $\mathbf{r}=(r_0,\ldots,r_{d-1})\in\operatorname{int}(\mathcal{D}_d)$ be a reduced parameter, and let $\mathcal{T}_{\mathbf{r}}(\mathbf{x})$ be the associated SRS tile for…