Derived sequences of complementary symmetric Rote sequences

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Derived sequences of complementary symmetric Rote sequences

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Derived sequences of complementary symmetric Rote sequences

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

RAIRO - Theoretical Informatics and Applications

ISSN

0988-3754

e-ISSN

1290-385X

Svazek periodika

53

Číslo periodika v rámci svazku

3-4

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

27

Strana od-do

125-151

Kód UT WoS článku

000508579100003

EID výsledku v databázi Scopus

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