Rich square-free words



: Vesti J

Publisher: ELSEVIER SCIENCE BV

: 2017

: Theoretical Computer Science

: THEORETICAL COMPUTER SCIENCE

: THEOR COMPUT SCI

: 687

: 48

: 61

: 14

: 0304-3975

: 1879-2294

DOI: https://doi.org/10.1016/j.tcs.2017.05.003


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.



Last updated on 2024-26-11 at 23:09