Partitioning the positive integers to seven Beatty sequences

DOI10.1016/S0019-3577(03)90000-0zbMath1052.11018OpenAlexW2052145361MaRDI QIDQ1433040

Péter Pál Varjú, János Barát

Publication date: 15 June 2004

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0019-3577(03)90000-0

zbMATH Keywords

covering systemBeatty sequenceFraenkel's conjectureperiodic balanced words

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Special sequences and polynomials (11B83) Symbolic dynamics (37B10) Arithmetic progressions (11B25)

Related Items (9)

On a generalization of Christoffel words: epichristoffel words ⋮ On the structure of bispecial Sturmian words ⋮ A different approach to the Fraenkel Conjecture for low $n$ values ⋮ A contribution to infinite disjoint covering systems ⋮ Webster sequences, apportionment problems, and just-in-time sequencing ⋮ Unnamed Item ⋮ On smooth sets of integers ⋮ Do balanced words have a short period? ⋮ Second Order Balance Property on Christoffel Words

Cites Work

• Unnamed Item
• Unnamed Item
• Unions of arithmetic sequences
• Covering the positive integers by disjoint sets of the form \(\{[n\alpha+\beta: n=1,2,\dots \}\)]
• Fraenkel's conjecture for six sequences
• Complementing and exactly covering sequences
• Balanced sequences and optimal routing
• Disjoint covering systems of rational Beatty sequences

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