The valuative capacity of subshifts of finite type

The characteristic sequence of a subset E of the integers enables to generalize the factorial. The asymptotic limit of this sequence, called the valuative capacity, is actually related to the transfinite diameter of this set embedded into the set of p-adic integers. We use tools of potential theory to obtain formulas to compute this capacity. As an example, we provide a family of sets, invariant by a family of graph-directed iterated function systems, whose valuative capacities are algebraic numbers.