Let be an ergodic translation on the compact group and a continuity set, i.e. a subset with topological boundary of Haar measure 0. An infinite binary sequence defined by if and otherwise, is called a Hartman sequence. In this talk we will study the growth rate of , where denotes the number of binary words of length occurring in . For the case that is an ergodic translation on the -dimensional torus we present a geometric method to calculate the asymptotic behaviour of .
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