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EXISTENCE OF AN INFINITE TERNARY 64-ABELIAN SQUARE-FREE WORD
Tekijät: Mari Huova
Kustantaja: EDP SCIENCES S A
Julkaisuvuosi: 2014
Journal: RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications
Tietokannassa oleva lehden nimi: RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS
Lehden akronyymi: RAIRO-THEOR INF APPL
Vuosikerta: 48
Numero: 3
Aloitussivu: 307
Lopetussivu: 314
Sivujen määrä: 8
ISSN: 0988-3754
DOI: https://doi.org/10.1051/ita/2014012
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.