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Morse and Hedlund’s skew Sturmian words revisited. (English) Zbl 1189.68089

Summary: For any infinite word \(r\) over \(A = \{a, b\}\) we associate two infinite words \(\min(r)\), \(\max(r)\) such that any prefix of \(\min(r)\) \((\max(r)\), respectively) is the lexicographically smallest (greatest, respectively) among the factors of \(r\) of the same length. We prove that \((\min(r)\); \(\max(r)) = (as, bs)\) for some infinite word \(s\) if and only if \(r\) is a proper Sturmian word or an ultimately periodic word of a particular form. This result is based on a lemma concerning sequences of infinite words.

MSC:

68R15 Combinatorics on words
37B10 Symbolic dynamics
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