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Systems of numeration. (English) Zbl 0545.10005
Computer arithmetic, Proc. 6th Symp., Aarhus/Den. 1983, 37-42 (1983).
[For the entire collection see Zbl 0533.00023.]
Let \(1=u_ 0<u_ 1<u_ 2<...\) be a finite or infinite sequence of integers. If we can represent a given integer \(N\) as \(\sum_{i}d_ iu_ i\) with \(d_ i\geq 0\) then the \(u_ i\) form a numeration system for \(N\). The author gives necessary and sufficient conditions for \(N\) to be representable uniquely, both when the \(u_ i\) are defined by a first-order recurrence relation (as e.g., in the decimal system) and by a higher-order relation (as, e.g., with Fibonacci systems). Applications of such systems to game-playing, tape-sorting, etc. are noted.
Reviewer: H.J.Godwin

MSC:
11A63 Radix representation; digital problems
05A05 Permutations, words, matrices
05C30 Enumeration in graph theory