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Currently displaying 1 – 2 of 2

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A test-set for $k$ -power-free binary morphisms

F. Wlazinski — 2001

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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 $k \geq 2$ , 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 $2 k + 1$

A test-set for -power-free binary morphisms

F. Wlazinski — 2010

RAIRO - Theoretical Informatics and Applications

A morphism is -power-free if and only if is -power-free whenever is a -power-free word. A morphism is -power-free up to if and only if is -power-free whenever is a -power-free word of length at most . Given an integer ≥ 2, we prove that a binary morphism is -power-free if and only if it is -power-free up to . This bound becomes linear for primitive morphisms: a binary primitive morphism is -power-free if and only if it is -power-free up to

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