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On Critical exponents in fixed points of k-uniform binary morphisms

Published online by Cambridge University Press:  20 December 2007

Dalia Krieger
Dalia Krieger*
Affiliation:
School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada; d2kriege@cs.uwaterloo.ca
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Abstract

Let w be an infinite fixed point of a binary k-uniform morphism f, and let Ew be the critical exponent of w. We give necessary and sufficient conditions for Ew to be bounded, and an explicit formula to compute it when it is. In particular, we show that Ew is always rational. We also sketch an extension of our method to non-uniform morphisms over general alphabets.

Keywords

Critical exponentbinary k-uniform morphism.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 1 , January 2009 , pp. 41 - 68
Copyright
© EDP Sciences, 2008

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