On Sturmian substitutions closed under derivation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F21%3A00353259" target="_blank" >RIV/68407700:21240/21:00353259 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21340/21:00353259

Výsledek na webu

<a href="https://doi.org/10.1016/J.TCS.2021.03.033" target="_blank" >https://doi.org/10.1016/J.TCS.2021.03.033</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/J.TCS.2021.03.033" target="_blank" >10.1016/J.TCS.2021.03.033</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Sturmian substitutions closed under derivation

Popis výsledku v původním jazyce

Occurrences of a factor $w$ in an infinite uniformly recurrent sequence ${bf u}$ can be encoded by an infinite sequence over a finite alphabet. This sequence is usually denoted ${bf d_{bf u}}(w)$ and called the derived sequence to $w$ in ${bf u}$. If $w$ is a prefix of a fixed point ${bf u}$ of a primitive substitution $varphi$, then by Durand's result from 1998, the derived sequence ${bf d_{bf u}}(w)$ is fixed by a primitive substitution $psi$ as well. For a non-prefix factor $w$, the derived sequence ${bf d_{bf u}}(w)$ is fixed by a substitution only exceptionally. To study this phenomenon we introduce a new notion: A finite set $M $ of substitutions is said to be closed under derivation if the derived sequence ${bf d_{bf u}}(w)$ to any factor $w$ of any fixed point ${bf u}$ of $varphi in M$ is fixed by a morphism $psi in M$. In our article we characterize the Sturmian substitutions which belong to a set $M$ closed under derivation. The characterization uses either the slope and the intercept of its fixed point or its S-adic representation.

Název v anglickém jazyce

On Sturmian substitutions closed under derivation

Popis výsledku anglicky

Occurrences of a factor $w$ in an infinite uniformly recurrent sequence ${bf u}$ can be encoded by an infinite sequence over a finite alphabet. This sequence is usually denoted ${bf d_{bf u}}(w)$ and called the derived sequence to $w$ in ${bf u}$. If $w$ is a prefix of a fixed point ${bf u}$ of a primitive substitution $varphi$, then by Durand's result from 1998, the derived sequence ${bf d_{bf u}}(w)$ is fixed by a primitive substitution $psi$ as well. For a non-prefix factor $w$, the derived sequence ${bf d_{bf u}}(w)$ is fixed by a substitution only exceptionally. To study this phenomenon we introduce a new notion: A finite set $M $ of substitutions is said to be closed under derivation if the derived sequence ${bf d_{bf u}}(w)$ to any factor $w$ of any fixed point ${bf u}$ of $varphi in M$ is fixed by a morphism $psi in M$. In our article we characterize the Sturmian substitutions which belong to a set $M$ closed under derivation. The characterization uses either the slope and the intercept of its fixed point or its S-adic representation.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Výzkumné centrum informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

1879-2294

Svazek periodika

867

Číslo periodika v rámci svazku

Květen

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

12

Strana od-do

128-139

Kód UT WoS článku

000640621200009

EID výsledku v databázi Scopus

2-s2.0-85103711197