Simultaneous avoidance of large squares and fractional powers in infinite binary words

Details Simultaneous avoidance of large squares and fractional powers in infinite binary words Simultaneous avoidance of large squares and fractional powers in infinite binary words

2003-04-29

arxiv.org/abs/math/0304476v1

Mathematics

Combinatorics

Scientific paper

In 1976, Dekking showed that there exists an infinite binary word that
contains neither squares yy with y >= 4 nor cubes xxx. We show that `cube' can
be replaced by any fractional power > 5/2. We also consider the analogous
problem where `4' is replaced by any integer. This results in an interesting
and subtle hierarchy.

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