Infinite words containing squares at every position

Details Infinite words containing squares at every position Infinite words containing squares at every position

2008-03-07

arxiv.org/abs/0803.1189v2

Mathematics

Combinatorics

12 pages; minor revisions and clarifications

Scientific paper

Richomme asked the following question: what is the infimum of the real
numbers $\alpha$ > 2 such that there exists an infinite word that avoids
$\alpha$-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 $\alpha$ = 7/3.

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