On stabilizers of infinite words

The stabilizer of an infinite word w over a finite alphabet is the monoid of morphisms over that fix w. In this paper we study various problems related to stabilizers and their generators. We show that over a binary alphabet, there exist stabilizers with at least n generators for all n. Over a ternary alphabet, the monoid of morphisms generating a given infinite word by iteration can be infinitely generated, even when the word is generated by iterating an invertible primitive morphism. Stabilizers of strict epistandard words are cyclic when non-trivial, while stabilizers of ultimately strict epistandard words are always non-trivial. For this latter family of words, we give a characterization of stabilizer elements.

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Dalia Krieger
• Keywords: Infinite Word, Stabilizers, Strict Epistandard Words, TCS 2008, Theoretical Computer Science