3 problems

Let $R$ be an $n\times n$ expanding integer matrix and let $0\in\mathcal D\subset\mathbb Z^n$ satisfy $\#\mathcal D=|\det(R)|$. Define $T(R,\mathcal D)$ to be the associated self-a…

Let $A$ be a dilation matrix and let $D$ be a centered canonical digit set for $A$, with attractor $T(A,D)$. A tile is called stretched when it has no $A$-invariant lattice of tran…

Let $A$ be an integer dilation matrix similar to a Jordan matrix $J\in M_m(\mathbb{Z})$, let $D_J$ be the centered canonical digit set for $J$, and choose an integer matrix $P$ giv…