Corrigendum : “Complexity of infinite words associated with beta-expansions”

Christiane Frougny; Zuzana Masáková; Edita Pelantová

Displaying similar documents to “Corrigendum : “Complexity of infinite words associated with beta-expansions””

Palindromic complexity of infinite words associated with non-simple Parry numbers

L&#039;ubomíra Balková, Zuzana Masáková (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

We study the palindromic complexity of infinite words $u_{β}$ , the fixed points of the substitution over a binary alphabet, $ϕ (0) = 0^{a} 1$ , $ϕ (1) = 0^{b} 1$ , with $a - 1 \geq b \geq 1$ , which are canonically associated with quadratic non-simple Parry numbers $β$ .

Complexity of infinite words associated with beta-expansions

Christiane Frougny, Zuzana Masáková, Edita Pelantová (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

We study the complexity of the infinite word $u_{β}$ associated with the Rényi expansion of $1$ in an irrational base $β > 1$ . When $β$ is the golden ratio, this is the well known Fibonacci word, which is sturmian, and of complexity $ℂ (n) = n + 1$ . For $β$ such that $d_{β} (1) = t_{1} t_{2} \dots t_{m}$ is finite we provide a simple description of the structure of special factors of the word $u_{β}$ . When $t_{m} = 1$ we show that $ℂ (n) = (m - 1) n + 1$ . In the cases when $t_{1} = t_{2} = \dots = t_{m - 1}$ or $t_{1} > max {t_{2}, \dots, t_{m - 1}}$ we show that the first difference of the complexity function $ℂ (n + 1) - ℂ (n)$ takes value in ${m - 1, m}$ for every $n$ , and consequently...

Sturmian jungle (or garden?) on multiliteral alphabets

L&amp;#039;ubomíra Balková, Edita Pelantová, Štěpán Starosta (2010)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

The properties characterizing sturmian words are considered for words on multiliteral alphabets. We summarize various generalizations of sturmian words to multiliteral alphabets and enlarge the list of known relationships among these generalizations. We provide a new equivalent definition of rich words and make use of it in the study of generalizations of sturmian words based on palindromes. We also collect many examples of infinite words to illustrate differences in the generalized...

Factor complexity of infinite words associated with non-simple Parry numbers.

Klouda, Karel, Pelantová, Edita (2009)

Integers

Similarity:

On possible growths of arithmetical complexity

Anna E. Frid (2006)

RAIRO - Theoretical Informatics and Applications

Similarity:

The arithmetical complexity of infinite words, defined by Avgustinovich, Fon-Der-Flaass and the author in 2000, is the number of words of length which occur in the arithmetical subsequences of the infinite word. This is one of the modifications of the classical function of subword complexity, which is equal to the number of factors of the infinite word of length . In this paper, we show that the orders of growth of the arithmetical complexity can behave as many sub-polynomial functions....

On some problems related to palindrome closure

Michelangelo Bucci, Aldo de Luca, Alessandro De Luca, Luca Q. Zamboni (2008)

RAIRO - Theoretical Informatics and Applications

Similarity:

In this paper, we solve some open problems related to (pseudo)palindrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if is an involutory antimorphism of , then the right and left -palindromic closures of any factor of a -standard word are also factors of some -standard word. We also introduce the class of pseudostandard words with “seed”, obtained by iterated pseudopalindrome closure...

Standard factors of Sturmian words

Gwénaël Richomme, Kalle Saari, Luca Q. Zamboni (2010)

RAIRO - Theoretical Informatics and Applications

Similarity:

Among the various ways to construct a characteristic Sturmian word, one of the most used consists in defining an infinite sequence of prefixes that are standard. Nevertheless in any characteristic word , some standard words occur that are not prefixes of . We characterize all standard words occurring in any characteristic word (and so in any Sturmian word) using firstly morphisms, then standard prefixes and finally palindromes.

Transcendence of numbers with an expansion in a subclass of complexity 2 + 1

Tomi Kärki (2006)

RAIRO - Theoretical Informatics and Applications

Similarity:

We divide infinite sequences of subword complexity into four subclasses with respect to left and right special elements and examine the structure of the subclasses with the help of Rauzy graphs. Let ≥ 2 be an integer. If the expansion in base of a number is an Arnoux-Rauzy word, then it belongs to Subclass I and the number is known to be transcendental. We prove the transcendence of numbers with expansions in the subclasses II and III.