Avoiding Squares and Overlaps Over the Natural Numbers

@article{GuayPaquet2009AvoidingSA,
  title={Avoiding Squares and Overlaps Over the Natural Numbers},
  author={Mathieu Guay-Paquet and Jeffrey Shallit},
  journal={Discrete Mathematics},
  year={2009},
  volume={309},
  pages={6245-6254}
}
We consider avoiding squares and overlaps over the natural numbers, using a greedy algorithm that chooses the least possible integer at each step; the word generated is lexicographically least among all such infinite words. In the case of avoiding squares, the word is 01020103 · · · , the familiar ruler function, and is generated by iterating a uniform morphism. The case of overlaps is more challenging. We give an explicitly-defined morphism φ : N∗ → N∗ that generates the lexicographically… CONTINUE READING

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Propriétés arithmétiques des substitutions et automates infinis

  • C. Mauduit
  • Ann. Inst. Fourier 56
  • 2006
1 Excerpt

Substitution dynamical systems on infinite alphabets

  • S. Ferenczi
  • Ann. Inst. Fourier 56
  • 2006
1 Excerpt

Sur la complexité de mots infinis engendrés par des q-automates dénombrables

  • M. Le Gonidec
  • Ann. Inst. Fourier 56
  • 2006
1 Excerpt

Axel Thue ’ s Papers on Repetitions in Words : a Translation . Number 20 in Publications du Laboratoire de Combinatoire et d ’ Informatique Mathématique

  • M. C. Er.
  • 1995

Thue’s Papers on Repetitions in Words: a Translation

  • J. Berstel. Axel
  • Number 20 in Publications du Laboratoire de…
  • 1995
1 Excerpt

The Towers of Hanoi and binary numerals

  • M. C. Er
  • J. Info. Optim. Sci. 6
  • 1985
1 Excerpt

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