Similarity density of the Thue-Morse word with overlap-free infinite binary words
arXiv:1405.5605 · doi:10.4204/EPTCS.151.16
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.
In Proceedings AFL 2014, arXiv:1405.5272