# Existence of an infinite ternary 64-abelian square-free word

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2014)

- Volume: 48, Issue: 3, page 307-314
- ISSN: 0988-3754

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topHuova, Mari. "Existence of an infinite ternary 64-abelian square-free word." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 48.3 (2014): 307-314. <http://eudml.org/doc/273016>.

@article{Huova2014,

abstract = {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.},

author = {Huova, Mari},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {combinatorics on words; k-abelian equivalence; square-freeness; -abelian; equivalence},

language = {eng},

number = {3},

pages = {307-314},

publisher = {EDP-Sciences},

title = {Existence of an infinite ternary 64-abelian square-free word},

url = {http://eudml.org/doc/273016},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Huova, Mari

TI - Existence of an infinite ternary 64-abelian square-free word

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 3

SP - 307

EP - 314

AB - 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.

LA - eng

KW - combinatorics on words; k-abelian equivalence; square-freeness; -abelian; equivalence

UR - http://eudml.org/doc/273016

ER -

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