Geodesic
The minimal density of a letter in an infinite ternary square-free word is \(0.2746 \cdots\)
Journal of integer sequences, Tome 5 (2002) no. 2
We study the minimal density of letters in infinite square-free words. First, we give some definitions of minimal density in infinite words and prove their equivalence. Further, we propose a method that allows to strongly reduce an exhaustive search for obtaining lower bounds for minimal density. Next, we develop a technique for constructing square-free morphisms with extremely small density for one letter that gives upper bounds on the minimal density. As an application of our technique we prove that the minimal density of any letter in infinite ternary square-free words is $0.2746 \dots $.
Classification : 11B05
Keywords: combinatorics on words, square-free word, factorial languages, minimal density (Concerned with sequence 
@article{JIS_2002__5_2_a7,
     author = {Tarannikov,  Yuriy},
     title = {The minimal density of a letter in an infinite ternary square-free word is \(0.2746 \cdots\)},
     journal = {Journal of integer sequences},
     year = {2002},
     volume = {5},
     number = {2},
     zbl = {1121.11303},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2002__5_2_a7/}
}
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Tarannikov,  Yuriy. The minimal density of a letter in an infinite ternary square-free word is \(0.2746 \cdots\). Journal of integer sequences, Tome 5 (2002) no. 2. http://geodesic.mathdoc.fr/item/JIS_2002__5_2_a7/