# 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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