Intersections of homogeneous Cantor sets and beta-expansions

Derong Kong, Wenxia Li, Michel Dekking

Let ${\Gamma }_{\beta ,N}$ be the $N$-part homogeneous Cantor set with $\beta \in (1/(2N-1),1/N)$. Any string $(j_{\ell }{)}_{\ell =1}^{\mathbb{N}}$ with $j_{\ell }\in \{0,\pm 1,...,\pm (N-1)\}$ such that $t=\sum_{\ell=1…