Geodesic
Improved bounds on the number of ternary square-free words
Journal of integer sequences, Tome 4 (2001) no. 2
Improved upper and lower bounds on the number of square-free ternary words are obtained. The upper bound is based on the enumeration of square-free ternary words up to length 110. The lower bound is derived by constructing generalised Brinkhuis triples. The problem of finding such triples can essentially be reduced to a combinatorial problem, which can efficiently be treated by computer. In particular, it is shown that the number of square-free ternary words of length n grows at least as 65^n/40, replacing the previous best lower bound of 2^n/17.
Classification : 05A15, 68R15, 05A20
Mots-clés : enumeration 
@article{JIS_2001__4_2_a6,
     author = {Grimm,  Uwe},
     title = {Improved bounds on the number of ternary square-free words},
     journal = {Journal of integer sequences},
     year = {2001},
     volume = {4},
     number = {2},
     zbl = {1004.05003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2001__4_2_a6/}
}
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Grimm,  Uwe. Improved bounds on the number of ternary square-free words. Journal of integer sequences, Tome 4 (2001) no. 2. http://geodesic.mathdoc.fr/item/JIS_2001__4_2_a6/