Abstract
Prefix normal words are binary words that have no factor with more 1s than the prefix of the same length. Finite prefix normal words were introduced in [Fici and Lipták, DLT 2011]. In this paper, we study infinite prefix normal words and explore their relationship to some known classes of infinite binary words. In particular, we establish a connection between prefix normal words and Sturmian words, between prefix normal words and abelian complexity, and between prefix normality and lexicographic order.
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Notes
- 1.
For ease of presentation, we use Lyndon to mean lexicographically greatest among its conjugates; this is equivalent to the usual definition up to renaming characters.
- 2.
Note the different terminology in [17]: characteristic word \(\rightarrow \) proper standard Sturmian, Sturmian \(\rightarrow \) proper Sturmian, rational mechanical word \(\rightarrow \) periodic Sturmian.
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Acknowledgements
We wish to thank the participants of the Workshop on Words and Complexity (Lyon, February 2018), for interesting discussions and pointers, and to Péter Burcsi, who first got us interested in Sturmian words.
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Cicalese, F., Lipták, Z., Rossi, M. (2019). On Infinite Prefix Normal Words. In: Catania, B., Královič, R., Nawrocki, J., Pighizzini, G. (eds) SOFSEM 2019: Theory and Practice of Computer Science. SOFSEM 2019. Lecture Notes in Computer Science(), vol 11376. Springer, Cham. https://doi.org/10.1007/978-3-030-10801-4_11
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