Episturmian words: a survey

Details Episturmian words: a survey Episturmian words: a survey

2008-01-10

arxiv.org/abs/0801.1655v2

RAIRO - Theoretical Informatics and Applications 43 (2009) 402-433

Mathematics

Combinatorics

36 pages; major revision: improvements + new material + more references

Scientific paper

10.1051/ita/2009003

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

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