Voir la notice de l'article provenant de la source Numdam
We survey several quantitative problems on infinite words related to repetitions, recurrence, and palindromes, for which the Fibonacci word often exhibits extremal behaviour.
@article{ITA_2008__42_4_701_0, author = {Cassaigne, Julien}, title = {On extremal properties of the {Fibonacci} word}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {701--715}, publisher = {EDP-Sciences}, volume = {42}, number = {4}, year = {2008}, doi = {10.1051/ita:2008003}, mrnumber = {2458702}, zbl = {1155.68062}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2008003/} }
TY - JOUR AU - Cassaigne, Julien TI - On extremal properties of the Fibonacci word JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2008 SP - 701 EP - 715 VL - 42 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita:2008003/ DO - 10.1051/ita:2008003 LA - en ID - ITA_2008__42_4_701_0 ER -
%0 Journal Article %A Cassaigne, Julien %T On extremal properties of the Fibonacci word %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2008 %P 701-715 %V 42 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita:2008003/ %R 10.1051/ita:2008003 %G en %F ITA_2008__42_4_701_0
Cassaigne, Julien. On extremal properties of the Fibonacci word. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 4, pp. 701-715. doi : 10.1051/ita:2008003. http://geodesic.mathdoc.fr/articles/10.1051/ita:2008003/
[1] Palindrome complexity. Theoret. Comput. Sci. 292 (2003) 9-31. | Zbl | MR
, , and ,[2] Transcendence of Sturmian or morphic continued fractions. J. Number Theory 91 (2001) 39-66. | Zbl | MR
, , and ,[3] On the index of Sturmian words, in Jewels are Forever. Springer, Berlin (1999) 287-294. | Zbl | MR
,[4] Initial powers of Sturmian sequences. Acta Arith. 122 (2006) 315-347. | Zbl | MR
, and ,[5] Enumeration of factors in the Thue-Morse word. Discrete Appl. Math. 24 (1989) 83-96. | Zbl | MR
,[6] On Dejean's conjecture over large alphabets. Theoret. Comput. Sci. 385 (2007) 137-151. | Zbl | MR
,[7] Special factors, periodicity, an application to Sturmian words. Acta Inform. 36 (2000) 983-1006. | Zbl | MR
and ,[8] Complexité et facteurs spéciaux. Bull. Belg. Math. Soc. Simon Stevin 4 (1997) 67-88. | Zbl | MR
,[9] On a conjecture of J. Shallit, in Automata, languages and programming (ICALP 1997), Springer, Berlin. Lect. Notes Comput. Sci. 1256 (1997) 693-704. | MR
,[10] Limit values of the recurrence quotient of Sturmian sequences. Theoret. Comput. Sci. 218 (1999) 3-12. | Zbl | MR
,[11] Fonctions de récurrence des suites d'Arnoux-Rauzy et réponse à une question de Morse et Hedlund. Ann. Inst. Fourier (Grenoble) 56 (2006) 2249-2270. | Zbl | MR | mathdoc-id
and ,[12] Dejean's conjecture and Sturmian words. Eur. J. Combin. 28 (2007) 876-890. Also in Morteza Mohammad-Noori, PhD. thesis, Université Paris-Sud (2005). | Zbl | MR
and ,[13] The index of Sturmian sequences. Eur. J. Combin. 23 (2002) 23-29. | Zbl | MR
and ,[14] Sur un théorème de Thue. J. Comb. Theory A 13 (1972) 90-99. | Zbl | MR
,[15] Palindromes and Sturmian words. Theoret. Comput. Sci. 223 (1999) 73-85. | Zbl | MR
and ,[16] On nonrepetitive sequences. J. Comb. Theory A 16 (1974) 159-164. | Zbl | MR
, and ,[17] Palindromic prefixes and episturmian words. J. Comb. Theory A 113 (2006) 1281-1304. | Zbl | MR
,[18] Algebraic combinatorics on words, Encyclopedia of Mathematics and its Applications 90. Cambridge University Press, Cambridge (2002). | Zbl | MR
,[19] Repetitions in the Fibonacci infinite word. RAIRO-Theor. Inf. Appl. 26 (1992) 199-204. | Zbl | MR | mathdoc-id
and ,[20] Periodicity and the golden ratio. Theoret. Comput. Sci. 204 (1998) 153-167. | Zbl | MR
, and ,[21] Recurrent geodesics on a surface of negative curvature. Trans. Amer. Math. Soc. 22 (1921) 84-100. | MR | JFM
,[22] Symbolic dynamics. Amer. J. Math. 60 (1938) 815-866. | MR | JFM
and ,[23] Symbolic dynamics II. Sturmian trajectories. Amer. J. Math. 62 (1940) 1-42. | MR | JFM
and ,[24] Proof of Dejean's conjecture for alphabets with 5, 6, 7, 8, 9, 10 and 11 letters. Theoret. Comput. Sci. 95 (1992) 187-205. | Zbl | MR
,[25] À propos d'une conjecture de F. Dejean sur les répétitions dans les mots. Discrete Appl. Math. 7 (1984) 297-311. | Zbl | MR
,[26] Mémoire sur quelques relations entre les puissances des nombres. C. R. Acad. Sci. Paris Sér. I 33 (1851) 225.
,[27] Suites à termes dans un alphabet fini, in Seminaire de théorie des nombres 1982-1983, Univ. Bordeaux I, 1983. Exposé 25. | Zbl | MR
,[28] Über unendliche Zeichenreihen. Norske Vid. Selsk. Skr., I. Mat. Nat. Kl., Christiana 7 (1906) 1-22. | JFM
,[29] Sturmian words and words with a critical exponent. Theoret. Comput. Sci. 242 (2000) 283-300. | Zbl | MR
,Cité par Sources :