a1 Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9, Canada; email@example.com, firstname.lastname@example.org
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.
(Online publication February 11 2010)
Mathematics Subject Classification: