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On-line \(q\)-adic covering by the method of the \(n\)-th segment and its application to on-line covering by cubes. (English) Zbl 0863.52010

The authors’ abstract: “We prove that in Euclidean \(d\)-space every sequence of cubes with total volume \(2^d+3\) is able to cover on-line the unit cube.
The proof is based on an on-line \(q\)-adic method of covering the unit segment by segments of lengths of the form \(q^{-r}\), where \(q\geq 2\) and \(r \geq 1\) are integers. The fact that this method is \(q\)-adic means that every segment has to be placed in such a way that both end-points are at points that are multiples of the length of the segment”.
Reviewer: H.-D.Hecker (Jena)

MSC:

52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
68W10 Parallel algorithms in computer science
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