Palindromic complexity of infinite words associated to simple Parry numbers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F06%3A00130589" target="_blank" >RIV/68407700:21340/06:00130589 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Palindromic complexity of infinite words associated to simple Parry numbers
Original language description
A simple Parry number is a real number $beta>1$ such that the R'enyi expansion of $1$ is finite, of the form $d_beta(1)=t_1 cdots t_m$. We study the palindromic structure of infinite aperiodic words $u_beta$ that are the fixed point of a substitution associated with a simple Parry number $beta$. It is shown that the word $u_beta$ contains infinitely many palindromes if and only if $t_1=t_2= cdots=t_{m-1}ge t_m$. Numbers $beta$ satisfying this condition are the so-called {em confluent} Pisot numbers. If $t_m=1$ then $u_beta$ is an Arnoux-Rauzy word. We show that if $beta$ is a confluent Pisot number then $ {mathcal P}(n+1)+ {mathcal P}(n) = {mathcal C}(n+1) - {mathcal C}(n) +2$, where ${mathcal P}(n)$ is the number of palindromes and ${mathcal C}(n)$ is the number of factors of length $n$ in $u_beta$. We then give a complete description of the set of palindromes, its structure and properties.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2006
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)