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- W3100508625 abstract "A finite word is closed if it contains a factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We are interested in the {it oc-sequence} of a word, which is the binary sequence whose $n$-th element is $0$ if the prefix of length $n$ of the word is open, or $1$ if it is closed. We exhibit results showing that this sequence is deeply related to the combinatorial and periodic structure of a word. In the case of Sturmian words, we show that these are uniquely determined (up to renaming letters) by their oc-sequence. Moreover, we prove that the class of finite Sturmian words is a maximal element with this property in the class of binary factorial languages. We then discuss several aspects of Sturmian words that can be expressed through this sequence. Finally, we provide a linear-time algorithm that computes the oc-sequence of a finite word, and a linear-time algorithm that reconstructs a finite Sturmian word from its oc-sequence." @default.
- W3100508625 created "2020-11-23" @default.
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- W3100508625 date "2017-09-01" @default.
- W3100508625 modified "2023-10-01" @default.
- W3100508625 title "The sequence of open and closed prefixes of a Sturmian word" @default.
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- W3100508625 doi "https://doi.org/10.1016/j.aam.2017.04.007" @default.
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