Abstract
We consider the (q, δ) numeration system, with basis q≥2 and the set of digits {δ, δ+1, … , q+δ−1} where −(q−1)≤δ≤0. We study properties of numbers where some digits do not occur. This is analogous to the Cantor set {0.a1a2⋯∣ai∈{0,2}}. We compute an asymptotic equivalent of the nth moment of the “Cantor (q, D)-distribution” which can be described as the numbers 0. w1w2… with wi∈D⊆{δ, … , q+δ−1}, and each such letter can occur with the same probability 1/Card D. Furthermore, we consider n random strings according to the distribution and the expected minimum of them. We find a recursion which we solve asymptotically.
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