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All Growth Rates of Abelian Exponents Are Attained by Infinite Binary Words Peltomäki, Jarkko Whiteland, Markus A. abelian equivalence abelian power abelian critical exponent 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: ℕ → 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jarkko Peltomäki and Markus A. Whiteland 2020 Is Part Of LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2020.79 urn:nbn:de:0030-drops-127481 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.79 eng https://creativecommons.org/licenses/by/3.0/legalcode