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arXiv · 1405.5605

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

Chen Fei Du·Jeffrey Shallit
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Abstract

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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Chen Fei Du, Jeffrey Shallit. 2014-05-22. Similarity density of the Thue-Morse word with overlap-free infinite binary words. https://doi.org/10.4204/eptcs.151.16

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