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