Derived Sequences of Arnoux—Rauzy Sequences

摘要

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