Partitioning the positive integers to seven Beatty sequences (Q1433040)
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scientific article; zbMATH DE number 2075405
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Partitioning the positive integers to seven Beatty sequences |
scientific article; zbMATH DE number 2075405 |
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Partitioning the positive integers to seven Beatty sequences (English)
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15 June 2004
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A conjecture of \textit{A. S. Fraenkel} [J. Comb. Theory, Ser. A 13, 8--20 (1973; Zbl 0257.05023)] on the decomposition of the set of positive integers into \(m\) disjoint Beatty sequences is proved for \(m=7\) using a balanced word technique developed and used previously by R. Tijdeman (\(m=3\)), E. Altman, B. Gaugal, A. Hordijk (\(m=4\)), and R. Tijdeman (\(m=5,6\)).
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covering system
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Beatty sequence
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periodic balanced words
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Fraenkel's conjecture
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