Talk:Square-free word
Latest comment: 10 years ago by Deltahedron in topic Disappointed
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Title
editIt would be good to change the title of this article from "Squarefree word" to "Square-free word", but I am not sure whether this is possible... —The preceding unsigned comment was added by Minashot (talk • contribs) 18:26, 23 November 2009 (UTC)
Disappointed
editI was disappointed when I came here to find the lack of content for this page in English, when I saw the vast amount of information provided on the French version of this page. — Preceding unsigned comment added by Cjripper (talk • contribs) 17:22, 15 March 2014 (UTC)
- Curiously enough, the same editor who expanded the French version more than tenfold also tagged it as being a stub article. I didn't take away much from it; once you have seen an example of an infinite square-free sequence, it is not particularly enlightening to see several more examples without any underlying theory tying any of this together. --Lambiam 00:52, 17 March 2014 (UTC)
- Thank you for expanding this. For theoretical documentation to help, I recommend "Non-repetitive Sequences" by P.A.B. Pleasants and "Combinatorics on Words" by Veikko Keränen. Cjripper (talk) 19:40, 19 March 2014 (UTC)
- I assume you mean Pleasants, P.A.B. (1971). "Non-repetitive sequences". In Atkin, A.O.L.; Birch, B.J. (eds.). Computers in Number Theory, Proc. Sci. Res. Council Atlas Sympos. No.2, Oxford 1969. London-New York: Academic Press. pp. 259–262. Zbl 0232.05004. That paper is about what are now called "abelian power-free words", words which avoid the repetition of subwords xyz... where each of x,y,z,... is a permutation of the others (abelian powers). This is a different concept to the subject of this article. For example, the paper cited shows that there are no abelian square-free words over an alphabet of size three: Keränen has shown that there is such a word over an alphabet of size four. Deltahedron (talk) 18:30, 20 March 2014 (UTC)