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

Mari Huova

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

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

Abstract

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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.

How to cite

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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 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 -

References

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