Geodesic
Infinite words containing squares at every position
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 113-124

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Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve this question in the case of a binary alphabet by showing that the answer is α = 7/3.

DOI : 10.1051/ita/2010007
Classification : 68R15
Keywords: infinite words, power-free words, squares 
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     author = {Currie, James and Rampersad, Narad},
     title = {Infinite words containing squares at every position},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {113--124},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {1},
     year = {2010},
     doi = {10.1051/ita/2010007},
     mrnumber = {2604937},
     zbl = {1184.68370},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2010007/}
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Currie, James; Rampersad, Narad. Infinite words containing squares at every position. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 113-124. doi: 10.1051/ita/2010007

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