scholarly journals A gap of the exponents of repetitions of Sturmian words

2021 ◽  
Vol 10 (3) ◽  
pp. 203-234
Author(s):  
Suzue Ohnaka ◽  
Takao Watanabe
Keyword(s):  
Sturmian Words

Sturmian words and overexponential codimension growth

2018 ◽  
Vol 95 ◽  
pp. 53-64
Author(s):  
Antonio Giambruno ◽  
Mikhail Zaicev
Keyword(s):  
Sturmian Words

scholarly journals Sturmian words, Lyndon words and trees

1997 ◽  
Vol 178 (1-2) ◽  
pp. 171-203 ◽  
Author(s):  
Jean Berstel ◽  
Aldo de Luca
Keyword(s):  
Sturmian Words ◽  
Lyndon Words

scholarly journals The Maximal Number of Runs in Standard Sturmian Words

10.37236/2473 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Paweł Baturo ◽  
Marcin Piątkowski ◽  
Wojciech Rytter
Keyword(s):  
Explicit Formula ◽  
Special Class ◽  
Linear Time ◽  
Infinite Sequence ◽  
Integer Sequence ◽  
Sturmian Word ◽  
Compact Representations ◽  
Sturmian Words ◽  
Standard Word

We investigate some repetition problems for a very special class $\mathcal{S}$ of strings called the standard Sturmian words, which  have very compact representations in terms of sequences of integers. Usually the size of this word is exponential with respect to the size of its integer sequence, hence we are dealing with repetition problems in compressed strings. An explicit formula is given for the number $\rho(w)$ of runs in a standard word $w$. We show that $\rho(w)/|w|\le 4/5$ for each $w\in S$, and  there is an infinite sequence of strictly growing words $w_k\in {\mathcal{S}}$ such that $\lim_{k\rightarrow \infty} \frac{\rho(w_k)}{|w_k|} = \frac{4}{5}$. Moreover, we show how to compute the number of runs in a standard Sturmian word in linear time with respect to the size of its compressed representation.

scholarly journals A geometrical approach of palindromic factors of standard billiard words

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Jean-Pierre Borel
Keyword(s):  
Geometrical Approach ◽  
International Audience ◽  
Sturmian Words

International audience Many results are already known, concerning the palindromic factors and the palindomic prefixes of Standard billiard words, i.e., Sturmian words and billiard words in any dimension, starting at the origin. We give new geometrical proofs of these results, especially for the existence in any dimension of Standard billiard words with arbitrary long palindromic prefixes.

scholarly journals Some Characterizations of Sturmian Words in Terms of the Lexicographic Order

2012 ◽  
Vol 116 (1-4) ◽  
pp. 25-33 ◽  
Author(s):  
Michelangelo Bucci ◽  
Alessandro De Luca ◽  
Luca Q. Zamboni
Keyword(s):  
Lexicographic Order ◽  
Sturmian Words

On the Index of Sturmian Words

1999 ◽  
pp. 287-294 ◽  
Author(s):  
Jean Berstel
Keyword(s):  
Sturmian Words

scholarly journals Studies on finite Sturmian words

2015 ◽  
Vol 591 ◽  
pp. 106-133 ◽  
Author(s):  
Christophe Reutenauer
Keyword(s):  
Sturmian Words
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