Document RAIRO-Theor. Inf. Appl. (2008)
DOI: 10.1051/ita:2007042
On Critical exponents in fixed points of k-uniform binary morphisms
Dalia KriegerSchool of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada; d2kriege@cs.uwaterloo.ca
(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
© EDP Sciences 2008