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2019 | OriginalPaper | Chapter

Derived Sequences of Arnoux–Rauzy Sequences

Author : Kateřina Medková

Published in: Combinatorics on Words

Publisher: Springer International Publishing

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Abstract

For an Arnoux–Rauzy sequence \(\mathbf {\mathbf u}\) we describe the set \(\text {Der}(\mathbf {\mathbf u})\) of derived sequences corresponding to all nonempty prefixes of \(\mathbf {\mathbf u}\) using the normalized directive sequence of \(\mathbf {\mathbf u}\). As a corollary, we show that all derived sequences of \(\mathbf {\mathbf u}\) are also Arnoux–Rauzy sequences. Moreover, if \(\mathbf {\mathbf u}\) is primitive substitutive, we precisely determine the cardinality of the set \(\text {Der}(\mathbf {\mathbf u})\).

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Literature
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Metadata
Title
Derived Sequences of Arnoux–Rauzy Sequences
Author
Kateřina Medková
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-030-28796-2_20

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