✦ LIBER ✦

Generalized Perturbed Symmetry

✍ Scribed by J.-P Allouche; J Shallit

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 161 KB
Volume: 19
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1998.0206

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✦ Synopsis

Let w R denote the reversal of the word w, and let w E = w. We examine a generalization of Mendès France's 'perturbed symmetry'. Specifically, we study a map of the form

where e i ∈ {E, R}, and the infinite word arising from iteration of this map. In particular, if the x i are fixed strings of identical length, the resulting infinite word is k-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.

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