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

Published online by Cambridge University Press:  10 July 2014

Mari Huova
Mari Huova*
Affiliation:
Department of Mathematics and Statistics & TUCS, University of Turku, 20014 Turku, Finland.. mari.huova@utu.fi
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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.

Keywords

Combinatorics on wordsk-abelian equivalencesquare-freeness
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 3: Special issue in the honor of the 14th “Journées montoises d’informatique théorique”. I. , July 2014 , pp. 307 - 314
Copyright
© EDP Sciences 2014

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