• Corpus ID: 119721523

On some problems of Harju concerning squarefree arithmetic progressions in infinite words

@article{Currie2018OnSP,
  title={On some problems of Harju concerning squarefree arithmetic progressions in infinite words},
  author={James D. Currie and Narad Rampersad},
  journal={arXiv: Combinatorics},
  year={2018}
}
In a recent paper, Harju posed three open problems concerning square-free arithmetic progressions in infinite words. In this note we solve two of them. 

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References

SHOWING 1-8 OF 8 REFERENCES
On square-free arithmetic progressions in infinite words
  • T. Harju
  • Mathematics
    Theor. Comput. Sci.
  • 2019
Infinite ternary square-free words concatenated from permutations of a single word
Multidimensional Unrepetitive Configurations
  • A. Carpi
  • Mathematics
    Theor. Comput. Sci.
  • 1988
Non-Repetitive Tilings
TLDR
A two-dimensional version of Axel Thue's result, showing how to construct a rectangular tiling of the plane using 5 symbols which has the property that lines of tiles which are horizontal, vertical or have slope +1 or $-1$ contain no repetitions.
ABELIAN COMPLEXITY OF FIXED POINT OF MORPHISM
TLDR
It is shown that the abelian complexity of vtm, i.e., the number of Parikh vectors of length n, is O (log n) with constant approaching 3 4 (assuming base 2 logarithm), and it is Ω (1) with constants 3 (and these are the best possible bounds).
Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen”, Norske Vid
  • Skrifter I. Mat.-Nat. Kl., Christiana
  • 1912
Sur la construction de mots sans carré
  • Séminaire de Théorie des Nombres 1978âĂŞ1979,
  • 1979