Geodesic
For each \(\alpha > 2\) there is an infinite binary word with critical exponent \(\alpha \)
The electronic journal of combinatorics, Tome 15 (2008)
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The critical exponent of an infinite word ${\bf w}$ is the supremum of all rational numbers $\alpha$ such that ${\bf w}$ contains an $\alpha$-power. We resolve an open question of Krieger and Shallit by showing that for each $\alpha > 2$ there is an infinite binary word with critical exponent $\alpha$.
DOI : 10.37236/909
Classification : 68R15
Mots-clés : combinatorics on words, repetitions, critical exponent 
@article{10_37236_909,
     author = {James D. Currie and Narad Rampersad},
     title = {For each \(\alpha > 2\) there is an infinite binary word with critical exponent \(\alpha \)},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/909},
     zbl = {1183.68439},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/909/}
}
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James D. Currie; Narad Rampersad. For each \(\alpha > 2\) there is an infinite binary word with critical exponent \(\alpha \). The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/909

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