On Critical exponents in fixed points of k-uniform binary morphisms
School of Computer Science, University of Waterloo,
Waterloo, ON N2L 3G1, Canada; firstname.lastname@example.org
Accepted: 23 October 2007
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.
Mathematics Subject Classification: 68R15
Key words: Critical exponent / binary k-uniform morphism.
© EDP Sciences, 2008