2 problems

Let $p,q,r$ be integers with absolute value at least $2$, let $s,t,a_i,b_j$ be real numbers, and define … and … Here $a_\infty$ and $b_\infty$ denote the limiting quantities used i…

Deng–Liu–Ngai conjecture. Under these hypotheses, the self-affine tile $T$ is homeomorphic to a $d$-dimensional ball if and only if its interior $T^\circ$ is connected. The conject…