MERCAS, R. and NOWOTKA, D., 2017. A note on Thue games. Information Processing Letters, 118 (February), pp. 75–77.
In this work we improve on a result from . In particular,
we investigate the situation where a word is constructed jointly by two
players who alternately append letters to the end of an existing word.
One of the players (Ann) tries to avoid (non-trivial) repetitions, while
the other one (Ben) tries to enforce them. We show a construction that
is closer to the lower bound showed in  using entropy compression, and
building on the probabilistic arguments based on a version of the Lov´asz
Local Lemma from . We provide an explicit strategy for Ann to avoid
(non-trivial) repetitions over a 7-letter alphabet.
This paper was accepted for publication in the journal Information Processing Letters and the definitive published version is available at http://dx.doi.org/10.1016/j.ipl.2016.10.004