Intersections of middle-$\alpha$ Cantor sets with a fixed translation

Yan Huang, Derong Kong

For $\lambda \in (0,1/3]$ let $C_{\lambda }$ be the middle-$(1-2\lambda )$ Cantor set in $\mathbb{R}$. Given $t\in [-1,1]$, excluding the trivial case we show that \[ Λ(t):=\left\{λ\in(0,1/3]: C_λ\cap(C_λ+t…