论文信息 - Generalized Perturbed Symmetry

Generalized Perturbed Symmetry

LetwRdenote the reversal of the wordw, and letwE=w. We examine a generalization of Mendes France's `perturbed symmetry?. Specifically, we study a map of the formS(w) = w?1? i? k?1xiwei,whereei ?{E,R}, and the infinite word arising from iteration of this map. In particular, if thexiare fixed strings of identical length, the resulting infinite word isk-automatic, and we characterize precisely when such a word can be ultimately periodic. Finally, we apply our technique to prove a 1994 conjecture by Blanchard and Fabre.

Jeffrey Shallit | Jean-Paul Allouche

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