Cyclically repetition-free words on small alphabets.

Harju, Tero and Nowotka, Dirk (2010) Cyclically repetition-free words on small alphabets. Information Processing Letters, 110 (14-15). pp. 591-595. DOI 10.1016/j.ipl.2010.05.005.

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Abstract

All sufficiently long binary words contain a square but there are infinite binary words having only the short squares 00, 11, and 0101. Recently, it was shown by J. Currie that there exist cyclically square-free words in a ternary alphabet except for lengths 5, 7, 9, 10, 14, and 17. We consider binary words all conjugates of which contain only short squares. We show that the number c(n) of these binary words of length n grows unboundedly. In order for this, we show that there are morphisms that preserve circular square-free words in the ternary alphabet.

Document Type: Article
Keywords: combinatorics on words repetitions conjugates square-free words cyclically square-free almost square-free words
Research affiliation: Kiel University
Refereed: Yes
Date Deposited: 01 Feb 2013 16:47
Last Modified: 23 Sep 2019 20:40
URI: https://oceanrep.geomar.de/id/eprint/20234

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