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On Infinite Prefix Normal Words
Ferdinando Cicalese1, Zsuzsanna Lipták1, Massimiliano Rossi2
1Department of Computer Science, University of Verona, Verona, Italy.
Abstract:
Prefix normal words are binary words with the property that no factor has 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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