Derived sequences of complementary symmetric Rote sequences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F19%3A00336584" target="_blank" >RIV/68407700:21340/19:00336584 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1051/ita/2019004" target="_blank" >https://doi.org/10.1051/ita/2019004</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1051/ita/2019004" target="_blank" >10.1051/ita/2019004</a>

Result language
angličtina
Original language name
Derived sequences of complementary symmetric Rote sequences
Original language description
Complementary symmetric Rote sequences are binary sequences which have factor complexity C(n) = 2n for all integers n >= 1 and whose languages are closed under the exchange of letters. These sequences are intimately linked to Sturmian sequences. Using this connection we investigate the return words and the derived sequences to the prefixes of any complementary symmetric Rote sequence v which is associated with a standard Sturmian sequence u. We show that any non-empty prefix of v has three return words. We prove that any derived sequence of v is coding of three interval exchange transformation and we determine the parameters of this transformation. We also prove that v is primitive substitutive if and only if u is primitive substitutive. Moreover, if the sequence u is a fixed point of a primitive morphism, then all derived sequences of v are also fixed by primitive morphisms. In that case we provide an algorithm for finding these fixing morphisms.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)