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On a paper by Castelli, Mignosi, Restivo

Jacques Justin
2000 RAIRO - Theoretical Informatics and Applications  
By induction assume it is true for 2, 3,..., t' -t -1.  ...  INTRODUCTION The Fine and Wilf theorem [5] is a well-known remarkable resuit in Combinatories on words [7] .  ... 
doi:10.1051/ita:2000122 fatcat:c6jzpuywpvhbxl4p52ez7l7z4a

Page 2787 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
Dong Yang Long (PRC-CHK-C; Kowloon) 68R_ Discrete mathematics in relation to computer science 20024:68090 2002d:68089 68R15 05A99 Justin, Jacques (F-PARIS7-FA; Paris) On a paper by M. Castelli, F.  ...  Mignosi, A. Restivo. Comment on: “Fine and Wilf’s theorem for three periods and a generalization of Sturmian words” [Theoret. Comput. Sci. 218 (1999), no. 1, 83-94; MR 2000c:68110].  ... 

Page 7287 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
Castelli, F. Mignosi and A. Restivo [Theoret. Comput. Sci. 218 (1999), no. 1, 83-94; MR 2000c:68110] studied the case of three periods, and J. Justin [Theor. Inform.  ...  In this paper we present a constructor for com- binatorial structures, called shuffle on trajectories (defined previ- ously in a non-combinatorial context [A. Mateescu, G. Rozenberg and A. K.  ... 

Page 2192 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews  
Gabriella (I-PLRM-AM; Palermo); Mignosi, Filippo (I-PLRM-AM; Palermo) ; Restivo, Antonio (I-PLRM-AM; Palermo) Fine and Wilf’s theorem for three periods and a generalization of Sturmian words.  ...  Patrice Séébold (Amiens) 2000c:68110 68R15 05A99 Castelli, M.  ... 

On the Contribution of WORDS to the Field of Combinatorics on Words [chapter]

Jean Néraud
2015 Lecture Notes in Computer Science  
summarizes the history of the conference WORDS, and the contributions which were presented, our goal being to testify how the conference may be embedded in the development of the field of Combinatorics on  ...  The notion of a partial word was introduced in WORDS 1997 by Jean Berstel Evidently each of the numerous results which were presented in the ten conferences plays a noticeable part in the state-of-the-field  ...  We will have achieved our goal if theses notes testify to the role of the WORDS conferences in the development of the field of Combinatorics on Words.  ... 
doi:10.1007/978-3-319-23660-5_3 fatcat:i6xrc7lnobdkrhwq3xib3rjvga

Fine and Wilf's theorem for three periods and a generalization of Sturmian words

M.Gabriella Castelli, Filippo Mignosi, Antonio Restivo
1999 Theoretical Computer Science  
We prove that the set 3-PER and the sequences of complexity 2n + 1, introduced by Amoux and Rauzy to generalize Sturmian words, have the same set of factors.  ...  This result is at origin of a deep investigation on the combinatorial properties of Sturmian words carried on in several papers (cf. [3, 7, 8, 181) .  ...  By Remark 5.1, for each good triple (~1, ~2, p3), S-PER contains exactly one word (up to a renaming).  ... 
doi:10.1016/s0304-3975(98)00251-5 fatcat:pgiztdzm4rcihpn4khrooptxbe

RECENT RESULTS ON EXTENSIONS OF STURMIAN WORDS

JEAN BERSTEL
2002 International journal of algebra and computation  
Sturmian words are infinite words over a two-letter alphabet that admit a great number of equivalent definitions. Most of them have been given in the past ten years.  ...  Acknowledgments I thank Jacques Justin and Jean Mairesse for helpful comments of an earlier version of this paper.  ...  Justin extends a result by Castelli, Mignosi and Restivo for three periods and shows Theorem 3.5.  ... 
doi:10.1142/s021819670200095x fatcat:skg3etiodncdxp2lne7ruex6cq

Fine and Wilf words for any periods II

R. Tijdeman, L.Q. Zamboni
2009 Theoretical Computer Science  
In the present paper the algorithm is extended in such a way that for any given positive integers n, p 1 , . . . , pr a word w of length n with periods p 1 , . . . , pr with a maximal number of distinct  ...  In 2003 the authors introduced a fast algorithm to determine the word w = w 1 ...wn of maximal length n, and with a maximal number of distinct letters for this length, such that w has prescribed periods  ...  Acknowledgement The authors would like to thank Danielle Heckman for many interesting discussions concerning the material in this paper.  ... 
doi:10.1016/j.tcs.2009.02.004 fatcat:tel3enzmkrfahgdzd4s7twmvuy

Page 1969 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
(English and French summaries) 202f:68141 — On a paper by M. Castelli, F. Mignosi, A. Restivo. Comment on: “Fine and Wilf’s theorem for three periods and a generalization of Sturmian words” [Theoret.  ...  (English summary) 2002b:68079 Mignosi, Filippo (with Zamboni, Luca Q.) On the number of Arnoux-Rauzy words. 2002k:68152 — (with Restivo, Antonio; Sciortino, M.) Words and forbidden factors.  ... 

Page 133 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
(with Tracy, Craig A.; Widom, Harold) Random words, Toeplitz determinants, and integrable systems. I. (English summary) 2002i:82040 Justin, Jacques On a paper by M. Castelli, F. Mignosi, A. Restivo.  ...  (English summary) 2002¢:68071 (Castelli, M. Gabriella) see Justin, Jacques, 2002d:68089 D'Alessandro, Flavio A combinatorial problem on trapezoidal words.  ... 

Page 909 of Mathematical Reviews Vol. , Issue Author Index [page]

Mathematical Reviews  
909 2002 AUTHOR INDEX — On a paper by M. Castelli, F. Mignosi, A. Restivo. Comment on: “Fine and Wilf’s theorem for three periods and a generalization of Sturmian words” [Theoret. Comput.  ...  (Alessandro Languasco) 2002d:11107 11M06 — (with Motohashi, Yoichi) A note on the mean value of the zeta and L-functions. XI. (English summary) Proc. Japan Acad. Ser. A Math.  ... 

Fine-Wilf graphs and the generalized Fine-Wilf theorem [article]

Stuart A. Rankin
2009 arXiv   pre-print
The Fine-Wilf theorem was generalized to finite sequences with three periods by M. G. Castelli, F. Mignosi, and A. Restivo, and in general by J. Justin, and even more broadly by R. Tijdeman and L.  ...  In this paper, we follow ideas introduced by S. Constantinescu and L.  ...  Nearly thirty-five years later (1999), the Fine-Wilf theorem was generalized to finite sequences with three periods by M. G. Castelli, F. Mignosi, and A. Restivo [1] .  ... 
arXiv:0906.1780v1 fatcat:ryproob6nnblrcdveqoy2hkhta

Lyndon words and Fibonacci numbers [article]

Kalle Saari
2012 arXiv   pre-print
In this paper we show that a much more accurate lower bound is log_phi(n) + 1, where phi denotes the golden ratio (1 + sqrt5)/2.  ...  We show that this bound is optimal in that it is attained by the Fibonacci Lyndon words.  ...  Lemma 1 (Castelli, Mignosi, and Restivo [4] ). Let w ∈ A + be a word with periods p, q. (i) If q < p ≤ |w|, then the prefix and suffix of w of length |w| − q have periods q and p − q.  ... 
arXiv:1207.4233v2 fatcat:3y3ot62m5fhodh45cbmlpc7lfm

Episturmian words: a survey

Amy Glen, Jacques Justin
2009 RAIRO - Theoretical Informatics and Applications  
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.  ...  After recalling definitions and basic properties, we consider episturmian morphisms that allow for a deeper study of these words.  ...  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