On Highly Repetitive and Power Free Words
Department of Mathematics and Statistics
University of Winnipeg
Department of Mathematics
University of Turku
Answering a question of Richomme, Currie and Rampersad proved that 7/3
is the infimum of the real numbers α > 2 such that there exists an
infinite binary word that avoids powers but is highly 2-repetitive,
i.e., contains arbitrarily large squares beginning at every position.
In this paper, we prove similar statements about β-repetitive words,
for some other β's, over the binary and the ternary alphabets.
Full version: pdf,
(Concerned with sequence
Received June 28 2012;
revised version received November 12 2012.
Published in Journal of Integer Sequences, March 2 2013.
Journal of Integer Sequences home page