We study the avoidance of Abelian powers of words and consider three reasonable generalizations of the notion of Abelian power to fractional powers. Our main goal is to find an Abelian analogue of the repetition threshold, , a numerical value separating -avoidable and -unavoidable Abelian powers for each size of the alphabet. We prove lower bounds for the Abelian repetition threshold for large alphabets and all definitions of Abelian fractional power. We develop a method estimating the exponential...
We study the avoidance of Abelian powers of words and consider three reasonable
generalizations of the notion of Abelian power to fractional powers. Our main goal is to
find an Abelian analogue of the repetition threshold, , a numerical
value separating -avoidable and -unavoidable Abelian
powers for each size of the alphabet. We prove lower bounds for the
Abelian repetition threshold for large alphabets and all definitions of Abelian fractional
...
The avoidability of binary patterns by binary cube-free words is investigated and the exact bound between unavoidable and avoidable patterns is found. All avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the growth rates of the avoiding languages are studied. All such languages, except for the overlap-free language, are proved to have exponential growth. The exact growth rates of languages avoiding minimal avoidable patterns are approximated through computer-assisted upper...
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