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Zbl 1010.68102
Wlazinski, F.
A test-set for $k$-power-free binary morphisms. (English)
[J] Theor. Inform. Appl. 35, No.5, 437-452 (2001). ISSN 0988-3754; ISSN 1290-385X/e

Summary: A morphism $f$ is $k$-power-free if and only if $f(w)$ is $k$-power-free whenever $w$ is a $k$-power-free word. A morphism $f$ is $k$-power-free up to $m$ if and only if $f(w)$ is $k$-power-free whenever $w$ is a $k$-power-free word of length at most $m$. Given an integer $k\ge 2$, we prove that a binary morphism is $k$-power-free if and only if it is $k$-power-free up to $k^2$. This bound becomes linear for primitive morphisms: a binary primitive morphism is $k$-power-free if and only if it is $k$-power-free up to $2k+1$.

MSC 2000:: *68R15 Combinatorics on words

Keywords: binary morphism

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