Geodesic
An improved lower bound on the number of ternary squarefree words
Journal of integer sequences, Tome 19 (2016) no. 6.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $s_{n}$ be the number of words in the ternary alphabet $\Sigma = {0, 1, 2}$ such that no subword (or factor) is a square (a word concatenated with itself, e.g., 11, 1212, and 102102). From computational evidence, the sequence $(s_{n})$ grows exponentially at a rate of about $1.317277^{n}$. While known upper bounds are already relatively close to the conjectured rate, effective lower bounds are much more difficult to obtain. In this paper, we construct a 54-Brinkhuis 952-triple, which leads to an improved lower bound on the number of $n$-letter ternary squarefree words: $952^{n/53}$ ≈ $1.1381531^{n}$.
Classification : 57M15, 11Y55 
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     author = {Sollami, Michael and Douglas, Craig C. and Liebmann, Manfred},
     title = {An improved lower bound on the number of ternary squarefree words},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
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Sollami, Michael; Douglas, Craig C.; Liebmann, Manfred. An improved lower bound on the number of ternary squarefree words. Journal of integer sequences, Tome 19 (2016) no. 6. http://geodesic.mathdoc.fr/item/JIS_2016__19_6_a5/