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On a paper by Castelli, Mignosi, Restivo

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] . ...

##
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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. ...

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

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

doi:10.1007/978-3-319-23660-5_3
fatcat:i6xrc7lnobdkrhwq3xib3rjvga
*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. ...##
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Fine and Wilf's theorem for three periods and a generalization of Sturmian words

1999
*
Theoretical Computer Science
*

We prove that the set 3-PER and the sequences of complexity 2n + 1, introduced

doi:10.1016/s0304-3975(98)00251-5
fatcat:pgiztdzm4rcihpn4khrooptxbe
*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). ...##
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RECENT RESULTS ON EXTENSIONS OF STURMIAN WORDS

2002
*
International journal of algebra and computation
*

Sturmian words are infinite words over

doi:10.1142/s021819670200095x
fatcat:skg3etiodncdxp2lne7ruex6cq
*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. ...##
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Fine and Wilf words for any periods II

2009
*
Theoretical Computer Science
*

In the present

doi:10.1016/j.tcs.2009.02.004
fatcat:tel3enzmkrfahgdzd4s7twmvuy
*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*. ...##
###
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. ...##
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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]

2009
*
arXiv
*
pre-print

The Fine-Wilf theorem was generalized to finite sequences with three periods

arXiv:0906.1780v1
fatcat:ryproob6nnblrcdveqoy2hkhta
*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] . ...##
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Lyndon words and Fibonacci numbers
[article]

2012
*
arXiv
*
pre-print

In this

arXiv:1207.4233v2
fatcat:3y3ot62m5fhodh45cbmlpc7lfm
*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. ...##
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Episturmian words: a survey

2009
*
RAIRO - Theoretical Informatics and Applications
*

In this

doi:10.1051/ita/2009003
fatcat:b2fwwhlldjftjmgruabyj45xr4
*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*. ...