License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2020.79
URN: urn:nbn:de:0030-drops-127481
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12748/
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Peltomäki, Jarkko ; Whiteland, Markus A.

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

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LIPIcs-MFCS-2020-79.pdf (0.4 MB)


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.

BibTeX - Entry

@InProceedings{peltomki_et_al:LIPIcs:2020:12748,
  author =	{Jarkko Peltom{\"a}ki and Markus A. Whiteland},
  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 =	{Javier Esparza and Daniel Kr{\'a}ľ},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12748},
  URN =		{urn:nbn:de:0030-drops-127481},
  doi =		{10.4230/LIPIcs.MFCS.2020.79},
  annote =	{Keywords: abelian equivalence, abelian power, abelian critical exponent}
}

Keywords: abelian equivalence, abelian power, abelian critical exponent
Collection: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Issue Date: 2020
Date of publication: 18.08.2020


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