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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
##### Citations:
Zbl 0537.05028; Zbl 0536.10009; Zbl 0533.00023