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Morse and Hedlund's Skew Sturmian Words Revisited
Giuseppe Pirillo1,2
1IASI, CNR, Viale Morgagni 67/A, 50134 Firenze, Italy
2Université de Marne-la-Vallée 5, boulevard Descartes Champs sur Marne, 77454 Marne-la- Vallée, Cedex 2, France
pirillo@math.unifi.it
Annals of Combinatorics 12 (1) p.115-121 March, 2008
AMS Subject Classification:94A45
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.
Keywords: words, lexicographic order, Sturmian words, episturmian words

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