All growth rates of abelian exponents are attained by infinite binary words



: Peltomäki Jarkko, Whiteland Markus A.

: Javier Esparza, Daniel Kráľ

: International Symposium on Mathematical Foundations of Computer Science

: 2020

: LIPICS – Leibniz international proceedings in informatics

: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

: LIPICS – Leibniz international proceedings in informatics

: 170

: 79:1

: 79:10

: 978-3-95977-159-7

DOI: https://doi.org/10.4230/LIPIcs.MFCS.2020.79

: https://research.utu.fi/converis/portal/detail/Publication/48627207


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.


Last updated on 2024-26-11 at 17:20