Abstract.
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.
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Received July 11, 2005
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Pirillo, G. Morse and Hedlund’s Skew Sturmian Words Revisited. Ann. Comb. 12, 115–121 (2008). https://doi.org/10.1007/s00026-008-0340-7
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DOI: https://doi.org/10.1007/s00026-008-0340-7