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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12748/
Peltomäki, Jarkko ;
Whiteland, Markus A.
All Growth Rates of Abelian Exponents Are Attained by Infinite Binary Words
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}
}
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Keywords: |
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abelian equivalence, abelian power, abelian critical exponent |
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Collection: |
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45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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18.08.2020 |
