## Special factors of automatic sequences.(English)Zbl 0856.11012

The author defines a special factor $$v$$ of an infinite sequence $$u$$ on a finite alphabet $$A$$ to be a finite factor (subblock) of $$u$$ such that, for each letter $$a\in A$$, the word $$va$$ is also a factor of $$u$$. Such words are sometimes called extendable, but note that a more general definition only assumes that $$va$$ is a factor for at least one letter $$a$$ [see for example: J. Cassaigne, Complexité et facteurs spéciaux, Bull. Belg. Math. Soc. (to appear)].
In order to study the special factors of infinite fixed points of morphisms, the author introduces the notion of rythmical word (essentially a word that is the “unique” image of another word by the morphism). Note that a recent paper by B. Mossé [Reconnaissabilité des substitutions et complexité des suites automatiques, Bull. Soc. Math. Fr. 124, 329-346 (1996; Zbl 0855.68072)] gives complementary results.

### MSC:

 11B85 Automata sequences 68R15 Combinatorics on words

Zbl 0855.68072
Full Text:

### References:

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