In this paper, we study a class $\mathcal{ A}(\lambda ,n,m)$ of self-similar sets with $m$ exact overlaps generated by $n$ similitudes of the same ratio $ \lambda $. We obtain a necessary condition for a self-similar set in $\mathcal{ A}(\lambda ,n,m)$ to be Lipschitz equivalent to a self-similar set satisfying the strong separation condition, i.e., there exists an integer $ k\geq 2$ such that $x^{ 2k}-mx^{ k}+n$ is reducible, in particular, $m$ belongs to $\{ a^{ i}:a\in \mathbb{ N}$ with $i\geq 2\}.$
Categories: math.DS math.MG