A4 Refereed article in a conference publication

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



Authors: Peltomäki Jarkko, Whiteland Markus A.

Editors: Javier Esparza, Daniel Kráľ

Conference name: International Symposium on Mathematical Foundations of Computer Science

Publication year: 2020

Journal: LIPICS – Leibniz international proceedings in informatics

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

Series title: LIPICS – Leibniz international proceedings in informatics

Volume: 170

First page : 79:1

Last page: 79:10

ISBN: 978-3-95977-159-7

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

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/48627207


Abstract

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.


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