\((q,\delta)\)-numeration systems with missing digits (Q1879308)

The authors consider the \((q,\delta)\) numeration system, with base \(q\geq 2\) and the set of digits \(\{\delta,\delta+1,\dots,q+\delta-1\}\) where \(-(q-1)\leq\delta\leq 0\). They study properties of numbers where some digits do not occur. Let \(D\) be a subset of the set above. Analogous to the Cantor set, they investigate an asymptotic behavior of the moment of the distribution which can be described as the numbers \(0.w_1 w_2\dots\) with \(w_i\in D\) and each letter in \(D\) appears with the same probability. They consider the expected minimum of \(n\) random strings according to the distribution, which is determined recursively.