Various Properties of Sturmian Words

P. Baláži

Abstract


This overview paper is devoted to Sturmian words. The first part summarizes different characterizations of Sturmian words. Besides the well known theorem of Hedlund and Morse it also includes recent results on the characterization of Sturmian words using return words or palindromes. The second part deals with substitution invariant Sturmian words, where we present our recent results. We generalize one-sided Sturmian words using the cut-and-project scheme and give a full characterization of substitution invariant Sturmian words. 

Keywords


Sturmian words; mechanical words; 2-interval exchange map; palindromes; return words; substitutions

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague