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 \(\text {Der}(\mathbf {\mathbf u})\).
This work was supported by the project CZ.02.1.01/0.0/0.0/16_019/0000778 from European Regional Development Fund and by the grant No. SGS17/193/OHK4/3T/14 from the Grant Agency of the CTU in Prague.
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Medková, K. (2019). Derived Sequences of Arnoux–Rauzy Sequences. In: Mercaş, R., Reidenbach, D. (eds) Combinatorics on Words. WORDS 2019. Lecture Notes in Computer Science(), vol 11682. Springer, Cham. https://doi.org/10.1007/978-3-030-28796-2_20
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DOI: https://doi.org/10.1007/978-3-030-28796-2_20
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