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DOI: 10.4230/LIPIcs.MFCS.2020.79

All Growth Rates of Abelian Exponents Are Attained by Infinite Binary Words

Authors: Jarkko Peltomäki and Markus A. Whiteland

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

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: 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.

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Jarkko Peltomäki and Markus A. Whiteland. All Growth Rates of Abelian Exponents Are Attained by Infinite Binary Words. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 79:1-79:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{peltomaki_et_al:LIPIcs.MFCS.2020.79,
  author =	{Peltom\"{a}ki, Jarkko and Whiteland, Markus A.},
  title =	{{All Growth Rates of Abelian Exponents Are Attained by Infinite Binary Words}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{79:1--79:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.79},
  URN =		{urn:nbn:de:0030-drops-127481},
  doi =		{10.4230/LIPIcs.MFCS.2020.79},
  annote =	{Keywords: abelian equivalence, abelian power, abelian critical exponent}
}

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All Growth Rates of Abelian Exponents Are Attained by Infinite Binary Words

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