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Following in the footsteps of P. Erdős, A. Rényi, and T. Šalát we compute the Hausdorff dimension of sets of numbers whose digits with respect to their -Cantor series expansions satisfy various statistical properties. In particular, we consider difference sets associated with various notions of normality and sets of numbers with a prescribed range of digits.
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Dylan Airey, Bill Mance, The Hausdorff dimension of sets of numbers defined by their -Cantor series expansions. J. Fractal Geom. 3 (2016), no. 2 pp. 163–186