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

Droubay, X.; Justin, J.; Pirillo, G.

Theor. Comput. Sci. 255, No. 1-2, 539-553 (2001).

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.

Reviewer: Jean-Paul Allouche (Orsay)

MSC:

68R15	Combinatorics on words
68Q45	Formal languages and automata

Keywords:

episturmian words; Sturmian words; palindrome factors; Rauzy rules; palindrome; episturmian morphisms

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