Infinite words containing squares at every position

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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.
12 pages; minor revisions and clarifications

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Combinatorics, Formal Languages and Automata Theory, 68R15

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http://salesiana.dossiersoluciones.com/handle/123456789/226636

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.1189
 http://arxiv.org/abs/0803.1189

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arXiv