A1 Refereed original research article in a scientific journal
Rich square-free words
Authors: Vesti J
Publisher: ELSEVIER SCIENCE BV
Publication year: 2017
Journal: Theoretical Computer Science
Journal name in source: THEORETICAL COMPUTER SCIENCE
Journal acronym: THEOR COMPUT SCI
Volume: 687
First page : 48
Last page: 61
Number of pages: 14
ISSN: 0304-3975
eISSN: 1879-2294
DOI: https://doi.org/10.1016/j.tcs.2017.05.003
Abstract
A word w is rich if it has vertical bar w vertical bar + 1 distinct palindromic factors, including the empty word. A word is square-free if it does not have a factor uu, where u is a non-empty word.Pelantova and Starosta (2013) [16] proved that every infinite rich word contains a square. We will give another proof for that result. Pelantova and Starosta marked with r(n) the length of a longest rich square-free word on an alphabet of size n. The exact value of r(n) was left as an open question. We will give an upper and a lower bound for r(n). The lower bound is conjectured to be exact but it is not explicit.We will also generalize the notion of repetition threshold for a limited class of infinite words. The repetition thresholds for episturmian and rich words are left as an open question. (C) 2017 Elsevier B.V. All rights reserved.
A word w is rich if it has vertical bar w vertical bar + 1 distinct palindromic factors, including the empty word. A word is square-free if it does not have a factor uu, where u is a non-empty word.Pelantova and Starosta (2013) [16] proved that every infinite rich word contains a square. We will give another proof for that result. Pelantova and Starosta marked with r(n) the length of a longest rich square-free word on an alphabet of size n. The exact value of r(n) was left as an open question. We will give an upper and a lower bound for r(n). The lower bound is conjectured to be exact but it is not explicit.We will also generalize the notion of repetition threshold for a limited class of infinite words. The repetition thresholds for episturmian and rich words are left as an open question. (C) 2017 Elsevier B.V. All rights reserved.
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