All growth rates of abelian exponents are attained by infinite binary words
Whiteland Markus A.; Peltomäki Jarkko
All growth rates of abelian exponents are attained by infinite binary words
Whiteland Markus A.
Peltomäki Jarkko
Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2021042827484
https://urn.fi/URN:NBN:fi-fe2021042827484
Tiivistelmä
We consider repetitions in infinite words by making a novel inquiry to the maximum eventual growth rate of the exponents of abelian powers occurring in an infinite word. Given an increasing, unbounded function $f\colon \N \to \R$, we construct an infinite binary word whose abelian exponents have limit superior growth rate $f$. As a consequence, we obtain that every nonnegative real number is the critical abelian exponent of some infinite binary word.
Kokoelmat
- Rinnakkaistallenteet [19207]