Similarity density of the Thue-Morse word with overlap-free infinite binary words

@inproceedings{Du2014SimilarityDO,
  title={Similarity density of the Thue-Morse word with overlap-free infinite binary words},
  author={Chen Fei Du and Jeffrey Shallit},
  booktitle={AFL},
  year={2014}
}
We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the Thue-Morse word t and its complement t bar, has this measure of similarity with t between 1/4 and 3/4. This is a partial generalization of a classical 1927 result of Mahler. 

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