Geodesic
Existence of an infinite ternary 64-abelian square-free word
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 307-314

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We consider a recently defined notion of k-abelian equivalence of words by concentrating on avoidance problems. The equivalence class of a word depends on the numbers of occurrences of different factors of length k for a fixed natural number k and the prefix of the word. We have shown earlier that over a ternary alphabet k-abelian squares cannot be avoided in pure morphic words for any natural number k. Nevertheless, computational experiments support the conjecture that even 3-abelian squares can be avoided over ternary alphabets. In this paper we establish the first avoidance result showing that by choosing k to be large enough we have an infinite k-abelian square-free word over three letter alphabet. In addition, this word can be obtained as a morphic image of a pure morphic word.

DOI : 10.1051/ita/2014012
Classification : 68R15
Keywords: combinatorics on words, k-abelian equivalence, square-freeness 
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     author = {Huova, Mari},
     title = {Existence of an infinite ternary 64-abelian square-free word},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {307--314},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     doi = {10.1051/ita/2014012},
     mrnumber = {3302490},
     zbl = {1297.68192},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2014012/}
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Huova, Mari. Existence of an infinite ternary 64-abelian square-free word. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 307-314. doi: 10.1051/ita/2014012

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