EPISTURMIAN WORDS: A SURVEY

In this paper, we survey the rich theory of infinite episturmianwords which generalize to any finite alphabet, in a rather resemblingway, the well-known family of Sturmian words on two letters.After recalling definitions and basic properties, we consider episturmianmorphisms that allow for a deeper study of these words. Some propertiesof factors are described, including factor complexity, palindromes,fractional powers, frequencies, and return words. We also consider lexicographicalproperties of episturmian words, as well as their connectionto the balance property, and related notions such as finite episturmianwords, Arnoux-Rauzy sequences, and “episkew words” that generalizethe skew words of Morse and Hedlund