Issue RAIRO-Theor. Inf. Appl. Volume 43, Number 1, January-March 2009 Page(s) 41 - 68 DOI 10.1051/ita:2007042 Published online 20 December 2007

RAIRO-Theor. Inf. Appl. 43, 41-68 (2009)
DOI: 10.1051/ita:2007042

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

Dalia Krieger

School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada; d2kriege@cs.uwaterloo.ca

Received November 2nd, 2006. Accepted October 23, 2007 Published online 20 December 2007

Abstract
Let w be an infinite fixed point of a binary k-uniform morphism f, and let E(w) be the critical exponent of w. We give necessary and sufficient conditions for E(w) to be bounded, and an explicit formula to compute it when it is. In particular, we show that E(w) 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.


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