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.2016.81
URN: urn:nbn:de:0030-drops-64892
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6489/
Rosenfeld, Matthieu
Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable
Abstract
We show that every binary pattern of length greater than 14 is abelian-2-avoidable. The best known upper bound on the length of abelian-2-unavoidable binary pattern was 118, and the best known lower bound is 7.
We designed an algorithm to decide, under some reasonable assumptions, if a morphic word avoids a pattern in the abelian sense. This algorithm is then used to show that some binary patterns are abelian-2-avoidable. We finally use this list of abelian-2-avoidable pattern to show our result. We also discuss the avoidability of binary patterns on 3 and 4 letters.
BibTeX - Entry
@InProceedings{rosenfeld:LIPIcs:2016:6489,
author = {Matthieu Rosenfeld},
title = {{Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable}},
booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
pages = {81:1--81:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-016-3},
ISSN = {1868-8969},
year = {2016},
volume = {58},
editor = {Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6489},
URN = {urn:nbn:de:0030-drops-64892},
doi = {10.4230/LIPIcs.MFCS.2016.81},
annote = {Keywords: combinatorics on words, pattern avoidance, abelian repetitions}
}
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Keywords: |
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combinatorics on words, pattern avoidance, abelian repetitions |
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Collection: |
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41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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19.08.2016 |
