Hausdorff dimension of the multiplicative golden mean shift
  We compute the Hausdorff dimension of the "multiplicative golden mean shift" defined as the set of all reals in $[0,1]$ whose binary expansion $(x_k)$ satisfies $x_k x_{2k}=0$ for all $k\ge 1$, and show that it is smaller than the Minkowski dimension. 
Richard Kenyon, Yuval Peres, and Boris Solomyak
math.DS math.NT