## Episturmian words and some constructions of de Luca and Rauzy.(English)Zbl 0981.68126

An infinite word $$s$$ on a finite alphabet is called episturmian standard if every left-most occurrence of a palindrome occurring in $$D$$ is a central subword (factor) of a palindrome prefix of $$s$$. An infinite word is called episturmian if it has exactly the same subwords (factors) as some episturmian standard word. The authors prove that an infinite word on a finite alphabet is episturmian if and only if its set of subwords is closed under reversal and contains at most one right special subword of each length. (Recall that a special subword is a subword $$w$$ such that $$wa$$ and $$wb$$ are also subwords for two distinct letters $$a$$, $$b$$.) In particular, the non-ultimately periodic episturmian words on a 2-letter alphabet are exactly the Sturmian words.
The authors give many nice properties of these infinite words as well as generalizations of the so-called Rauzy rules and a study of episturmian morphisms.

### MSC:

 68R15 Combinatorics on words 68Q45 Formal languages and automata
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### References:

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