  We compute the Hausdorff and Minkowski dimension of subsets of the symbolic
space $\Sigma_m=\{0,...,m-1\}^\N$ that are invariant under multiplication by
integers. The results apply to the sets $\{x\in \Sigma_m: \forall\, k, \ x_k
x_{2k}... x_{n k}=0\}$, where $n\ge 3$. We prove that for such sets, the
Hausdorff and Minkowski dimensions typically differ.
