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Decimations and sturmian words

Jacques Justin, Giuseppe Pirillo
1997 RAIRO - Theoretical Informatics and Applications  
Then a) an infinité word is standard proper Sturmian if and only if it has an irrational density and is invariant under A p ; b) an infinité word can be deduced from a standard periodic Sturmian word in  ...  Informatique théorique et Applications/Theoretical Informaties and Applications vol. 31, n° 3, 1997 PROPOSITION 7: G/ven a proper Sturmian word s, let u be a word SUL t mai u ^ Fac(s) and  ... 
doi:10.1051/ita/1997310302711 fatcat:dtvwoutlyzhmxbpguvpe7qtfaq

Some characterizations of finite Sturmian words

Aldo de Luca, Alessandro De Luca
2006 Theoretical Computer Science  
In this paper, we give some new characterizations of words which are finite factors of Sturmian words. An enumeration formula for primitive finite Sturmian words is given.  ...  Moreover, we provide two linear-time algorithms to recognize whether a finite word is Sturmian.  ...  Acknowledgments We wish to thank Jean Berstel and Arturo Carpi for their suggestions and helpful comments.  ... 
doi:10.1016/j.tcs.2006.01.036 fatcat:nt3cll62t5akzdehkw54gb67fu

A Note on a Conjecture of Duval and Sturmian Words

Filippo Mignosi, Luca Q. Zamboni
2002 RAIRO - Theoretical Informatics and Applications  
These notions extend directly to infinite words. For an infinite word ω, if µ(ω) is finite, then ω is periodic of period µ(ω). (cf. [2] and [4]).  ...  We prove a long standing conjecture of Duval in the special case of Sturmian words. Let U be a nonempty word on a finite alphabet A.  ...  In this note we verify Duval's conjecture in the special case that U is an unbordered Sturmian word, that is when U is an unbordered factor of an infinite Sturmian word on {0, 1}.  ... 
doi:10.1051/ita:2002001 fatcat:fu6h3w7xuzd5tks2nozr3sxlti

Palindromes in Sturmian Words [chapter]

Aldo de Luca, Alessandro De Luca
2005 Lecture Notes in Computer Science  
We study some structural and combinatorial properties of Sturmian palindromes, i.e., palindromic finite factors of Sturmian words.  ...  In particular, we give a formula which permits to compute in an exact way the number of Sturmian palindromes of any length.  ...  Introduction Sturmian words have been widely studied for their theoretical importance and their applications to various fields of science.  ... 
doi:10.1007/11505877_18 fatcat:oeiwubo6iva4doysc2k72noqky

Page 2100 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
The paper contains a characterization of epi-Sturmian words in terms of special right factors, and a computation of the complexity function of these words: Up to an additive constant, the complex- ity  ...  Next, the authors define an infinite word to be standard epi- Sturmian if the set of its prefixes is closed under taking right palindromic closures; and to be epi-Sturmian if it has the same set of factors  ... 

Relation between powers of factors and the recurrence function characterizing Sturmian words

Z. Masáková, E. Pelantová
2009 Theoretical Computer Science  
Carpi, A. de Luca, Special factors, periodicity, and an application to Sturmian words, Acta Inform. 36 (2000) 983-1006] and [D. Damanik, D. Lenz, The index of Sturmian sequences, European J.  ...  In this paper we use the relation of the index of an infinite aperiodic word and its recurrence function to give another characterization of Sturmian words.  ...  Acknowledgements We are grateful to J.-P. Allouche for pointing out the reference [7] .  ... 
doi:10.1016/j.tcs.2009.04.003 fatcat:qsialo6prbga3bvovbl7zet7eu

COMBINATORIAL PROPERTIES OF STURMIAN PALINDROMES

ALDO DE LUCA, ALESSANDRO DE LUCA
2006 International Journal of Foundations of Computer Science  
We study some structural and combinatorial properties of Sturmian palindromes, i.e., palindromic finite factors of Sturmian words.  ...  In particular, we give a formula which permits to compute in an exact way the number of Sturmian palindromes of any length.  ...  The work for this paper was partially supported by the Italian Ministry of Education under project COFIN 2003 "Formal Languages and Automata: methods, models and applications" and by the Faculty of Science  ... 
doi:10.1142/s0129054106003991 fatcat:keok4e7zurhync2pzazsnu5kum

Extremal properties of (epi)Sturmian sequences and distribution modulo 1 [article]

Jean-Paul Allouche, Amy Glen
2009 arXiv   pre-print
Dubickas (2005) on a question in distribution of real numbers modulo 1 via combinatorics on words, we survey some combinatorial properties of (epi)Sturmian sequences and distribution modulo 1 in connection  ...  to their work.  ...  Acknowledgements The authors would like to thank J. Berstel, J. Cassaigne, J. Justin, D. Kwon, G. Pirillo, G. Richomme, P. Séébold, and L. Q. Zamboni for discussions, comments, and suggestions.  ... 
arXiv:0907.2430v1 fatcat:pgo6wxba75f4bpbmpwwkg4g4by

Extremal properties of (epi)Sturmian sequences and distribution modulo $1$

Jean-Paul Allouche, Amy Glen
2010 L'Enseignement mathématique  
Dubickas (2005) on a question in distribution of real numbers modulo 1 via combinatorics on words, we survey some combinatorial properties of (epi)Sturmian sequences and distribution modulo 1 in connection  ...  to their work.  ...  About combinatorics of words and Lorenz maps [10, 11, 12, 13, 56, 81] , about extremal properties of Sturmian sequences or measures [21, 48, 58, 59] , about the distribution of {ξα n } [2, 3, 32, 87,  ... 
doi:10.4171/lem/56-3-5 fatcat:alduzkemubhdpm6cyivfotmwxi

On Sturmian substitutions closed under derivation [article]

Edita Pelantová, Štěpán Starosta
2019 arXiv   pre-print
Occurrences of a factor w in an infinite uniformly recurrent sequence u can be encoded by an infinite sequence over a finite alphabet.  ...  In our article we characterize the Sturmian substitutions which belong to a set M closed under derivation.  ...  To conclude, the return words of w and ws are identical, and thus so are the derived words with respect to w and ws. Item (2): The factor w is a factor of some left special factor.  ... 
arXiv:1908.11095v1 fatcat:hnhtzah6fnbvhoxl5gxfowjdr4

Relation between powers of factors and recurrence function characterizing Sturmian words [article]

Zuzana Masáková, Edita Pelantová
2008 arXiv   pre-print
In this paper we use the relation of the index of an infinite aperiodic word and its recurrence function to give another characterization of Sturmian words.  ...  As a byproduct, we give a new proof of theorem describing the index of a Sturmian word in terms of the continued fraction expansion of its slope.  ...  Acknowledgements We are grateful to J.-P. Allouche for pointing out the reference [7] .  ... 
arXiv:0809.0603v2 fatcat:fqmxeph4ingi5dvausif4ib254

Fixed points of Sturmian morphisms and their derivated words [article]

Karel Klouda, Kateřina Medková, Edita Pelantová, and Štěpán Starosta
2018 arXiv   pre-print
We provide an algorithm which to a given Sturmian morphism ψ lists the morphisms fixing the derivated words of the Sturmian word u = ψ( u). We provide a sharp upper bound on length of the list.  ...  Ordering of the return words to w in this concatenation is coded by derivated word d_ u(w).  ...  An infinite word u is eventually periodic if and only if L(u) contains only finitely many right special factors.  ... 
arXiv:1801.09203v3 fatcat:dvuyiacmwna6vnur6rol2w3ii4

Episturmian words: a survey

Amy Glen, Jacques Justin
2009 RAIRO - Theoretical Informatics and Applications  
Some properties of factors are described, including factor complexity, palindromes, fractional powers, frequencies, and return words.  ...  In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of Sturmian words on two letters.  ...  The authors would like to thank Jean Berstel and Pierre Arnoux for their helpful comments on a preliminary version of this paper.  ... 
doi:10.1051/ita/2009003 fatcat:b2fwwhlldjftjmgruabyj45xr4

Sturmian words and a criterium by Michaux–Villemaire

Isabel M. Araújo, Véronique Bruyère
2005 Theoretical Computer Science  
Michaux and Villemaire's proof of Cobham's theorem relies on the characterization of ultimately periodic words by means of the behaviour of certain repetitions in the word.  ...  In this paper we study those properties for characteristic Sturmian words. In particular we answer a question posed by Michaux and Villemaire in that context. (I.M.  ...  Acknowledgements We are thankful to Jean Berstel and Valérie Berthé for helpful discussions.  ... 
doi:10.1016/j.tcs.2005.01.010 fatcat:d6tdneyl3bhrtbtiig5yv66k44

A remark on morphic sturmian words

J. Berstel, P. Séébold
1994 RAIRO - Theoretical Informatics and Applications  
The following conditions are equivalent: (i) x is Sturmian; (ii) x is balanced and not ultimately periodic; (iii) there exist an irrational number a (0 < a < 1) and a real p such that A Sturmian word x  ...  In this Note, we prove a combinatorial property of a special class of morphic words, namely morphic Sturmian words. The property is best explained by an example.  ... 
doi:10.1051/ita/1994283-402551 fatcat:vvkgljo7k5gyzipgcgcxbgxmpe
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