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Infinite words containing squaresat every position

Published online by Cambridge University Press:  11 February 2010

James Currie and
Narad Rampersad
James Currie
Affiliation:
Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9, Canada; j.currie@uwinnipeg.ca, n.rampersad@uwinnipeg.ca
Narad Rampersad
Affiliation:
Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9, Canada; j.currie@uwinnipeg.ca, n.rampersad@uwinnipeg.ca
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Abstract

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

Keywords

Infinite wordspower-free wordssquares.

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