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

Published online by Cambridge University Press:  15 August 2002

F. Wlazinski
F. Wlazinski*
Affiliation:
LaRIA, Université de Picardie Jules Verne, 5 rue du Moulin Neuf, 80000 Amiens, France; wlazinsk@laria.u-picardie.fr.
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Abstract

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 ≥ 2, we prove that a binary morphism is k-power-free if and only if it is k-power-free up to k2. 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

Keywords

Combinatorics on wordsk-power-free wordsmorphismstest-sets
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 5 , September 2001 , pp. 437 - 452
Copyright
© EDP Sciences, 2001

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