On extremal properties of the Fibonacci word

 Access to full text

 Full (PDF)

 Access to full text

 Full (PDF)

1. J.-P. Allouche, M. Baake, J. Cassaigne and D. Damanik, Palindrome complexity. Theoret. Comput. Sci.292 (2003) 9–31.  
2. J.-P. Allouche, J.L. Davison, M. Queffélec and L.Q. Zamboni, Transcendence of Sturmian or morphic continued fractions. J. Number Theory91 (2001) 39–66.  
3. J. Berstel, On the index of Sturmian words, in Jewels are Forever. Springer, Berlin (1999) 287–294.  
4. V. Berthé, C. Holton and L.Q. Zamboni, Initial powers of Sturmian sequences. Acta Arith.122 (2006) 315–347.  
5. S. Brlek, Enumeration of factors in the Thue-Morse word. Discrete Appl. Math.24 (1989) 83–96.  
6. A. Carpi, On Dejean's conjecture over large alphabets. Theoret. Comput. Sci.385 (2007) 137–151.  
7. A. Carpi and A. de Luca, Special factors, periodicity, an application to Sturmian words. Acta Inform.36 (2000) 983–1006.  
8. J. Cassaigne, Complexité et facteurs spéciaux. Bull. Belg. Math. Soc. Simon Stevin4 (1997) 67–88.  
9. J. Cassaigne, On a conjecture of J. Shallit, in Automata, languages and programming (ICALP 1997), Springer, Berlin. Lect. Notes Comput. Sci.1256 (1997) 693–704.  
10. J. Cassaigne, Limit values of the recurrence quotient of Sturmian sequences. Theoret. Comput. Sci.218 (1999) 3–12.  
11. J. Cassaigne and N. Chekhova, 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.  
12. J.D. Currie and M. Mohammad-Noori, Dejean's conjecture and Sturmian words. Eur. J. Combin.28 (2007) 876–890. Also in Morteza Mohammad-Noori, PhD. thesis, Université Paris-Sud (2005).  
13. D. Damanik and D. Lenz, The index of Sturmian sequences. Eur. J. Combin.23 (2002) 23–29.  
14. F. Dejean, Sur un théorème de Thue. J. Comb. Theory A13 (1972) 90–99.  
15. X. Droubay and G. Pirillo, Palindromes and Sturmian words. Theoret. Comput. Sci.223 (1999) 73–85.  
16. R.C. Entringer, D.E. Jackson and J.A. Schatz, On nonrepetitive sequences. J. Comb. Theory A16 (1974) 159–164.  
17. S. Fischler, Palindromic prefixes and episturmian words. J. Comb. Theory A113 (2006) 1281–1304.  
18. M. Lothaire, Algebraic combinatorics on words, Encyclopedia of Mathematics and its Applications90. Cambridge University Press, Cambridge (2002).  
19. F. Mignosi and G. Pirillo, Repetitions in the Fibonacci infinite word. RAIRO-Theor. Inf. Appl.26 (1992) 199–204.  
20. F. Mignosi, A. Restivo and S. Salemi, Periodicity and the golden ratio. Theoret. Comput. Sci.204 (1998) 153–167.  
21. M. Morse, Recurrent geodesics on a surface of negative curvature. Trans. Amer. Math. Soc.22 (1921) 84–100.  
22. M. Morse and G.A. Hedlund, Symbolic dynamics. Amer. J. Math.60 (1938) 815–866.  
23. M. Morse and G.A. Hedlund, Symbolic dynamics II. Sturmian trajectories. Amer. J. Math.62 (1940) 1–42.  
24. J. Moulin-Ollagnier, Proof of Dejean's conjecture for alphabets with 5, 6, 7, 8, 9, 10 and 11 letters. Theoret. Comput. Sci.95 (1992) 187–205.  
25. J.-J. Pansiot, À propos d'une conjecture de F. Dejean sur les répétitions dans les mots. Discrete Appl. Math.7 (1984) 297–311.  
26. É. Prouhet, Mémoire sur quelques relations entre les puissances des nombres. C. R. Acad. Sci. Paris Sér. I33 (1851) 225.  
27. G. Rauzy, Suites à termes dans un alphabet fini, in Seminaire de théorie des nombres 1982–1983, Univ. Bordeaux I, 1983. Exposé 25.  
28. A. Thue, Über unendliche Zeichenreihen. Norske Vid. Selsk. Skr., I. Mat. Nat. Kl., Christiana7 (1906) 1–22.  
29. D. Vandeth, Sturmian words and words with a critical exponent. Theoret. Comput. Sci.242 (2000) 283–300.  

1. Juhani Karhumäki, Svetlana Puzynina, Locally catenative sequences and Turtle graphics
2. Juhani Karhumäki, Svetlana Puzynina, Locally catenative sequences and Turtle graphics
3. Artūras Dubickas, Squares and cubes in Sturmian sequences
4. Gwénaël Richomme, Kalle Saari, Luca Q. Zamboni, Standard factors of Sturmian words