Palindromes and Sturmian words

Theoretical Computer Science

Volumn 223, Issue 1-2, 1999, Pages 73-85

  Droubay, Xavier ^a   Pirillo, Giuseppe ^b  

^a UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

^b CNR   (Italy)

Author keywords

Morphisms; Palindromes; Standard words; Sturmian words; Subword complexity

Indexed keywords

EID: 0002255421     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(97)00188-6     Document Type: Article

References (31)

1. J.P. Allouche, Sur la complexité des suites infinies, Bull. Belgian Math. Soc. 1 (1994) 133-143.
2. J. Berstel, Recent results in Sturmian words, in: J. Dassaw (Ed.), Proc. 2nd Internat. Conf. Developments in Language Theory. World Scientific, Singapore, 1995.
3. J. Berstel and A. de Luca, Sturmian words, Lyndon words and trees, Theoret. Comput. Sci. 178 (1-2) (1997) 171-203.
4. J. Berstel, P. Séébold, A characterization of Sturmian morphisms, in: A. Borzyskovski, S. Sokolovski (Eds.), Proc. 21st Internat. Symp. on MFCS, Lecture Notes Computer Science, vol. 711, Springer, Berlin, 1993, pp. 281-290.
5. J. Berstel, P. Séébold, A remark on morphic Sturmian words, Theoret. Inform. Appl. 28 (1994) 255-263.
6. T.C. Brown, Descriptions of the characteristic sequence of an irrational, Canad. Math. Bull. 36 (1993) 15-21.
7. W.-F. Chuan, Symmetric Fibonacci words, Fibonacci Quart. 31 (1993) 251-255.
8. E. Coven, G.A. Hedlund, Sequences with minimal block growth, Math. System Theory 7 (1973) 138-153.
9. D. Crisp, W. Moran, A. Pollington, P. Shiue, Substitution invariant cutting sequences, J. de Théorie des Nombres de Bordeaux 5 (1993) 123-138.
10. K. Culik II, J. Kharumäki, Iterative devices generating infinite words, Internat. J. Algebra Comput. 5 (1994) 69-97.
11. A. de Luca, A combinatorial property of the Fibonacci words, Inform. Process. Lett. 12 (1981) 193-195.
12. A. de Luca, On Standard Sturmian morphisms, Theoret. Comput. Sci. 178 (1-2) (1997) 205-224.
13. A. de Luca, Sturmian words: structure, combinatorics, and their arithmetics, Theoret. Comput. Sci., to appear.
14. A. de Luca, F. Mignosi, Some combinatorial properties of Sturmian words, Theoret. Comput. Sci. 136 (1994) 361-385.
15. X. Droubay, Palindromes in the Fibonacci word, Inform. Process. Lett. 55 (1995) 217-221.
16. S. Dulucq, D. Gouyou-Beauchamps, Sur les facteurs des suites de Sturm, Theoret. Comput. Sci. 71 (1990) 381-400.
17. G.A. Hedlund, Sturmian minimal sets, Amer. J. Math. 66 (1944) 605-620.
18. G.A. Hedlund, M. Morse, Symbolic dynamics II: Sturmian sequences, Amer. J. Math. 61 (1940) 1-42.
19. J. Justin, G. Pirillo, Decimations and Sturmian words, Rapport interne de l'Institut Gaspard Monge, 97-07.
20. J. Justin, G. Pirillo, On a combinatorial property of Sturmian words, Theoret. Comput. Sci. 154 (1996) 387-394.
21. M. Lothaire, Combinatorics on words, in: Encyclopedia of Mathematics and its Applications, vol. 17, Addison-Wesley, Reading, MA, 1983.
22. A.A. Markoff, Sur une question de Jean Bernoulli, Math. Ann. 19 (1882) 27-36.
23. F. Mignosi, Infinite words with linear subword complexity, Theoret. Comput. Sci. 65 (1989) 221-242.
24. F. Mignosi, P. Séébold, Morphismes Sturmiens et règles de Rauzy, J. de Théorie des Nombres de Bordeaux 5 (1993) 221-233.
25. G. Pirillo, Some remarks on the Fibonacci word, Research Institute for Mathematical Sciences, Kyoto (1995).
26. G. Pirillo, Fibonacci Numbers and words, Actes du Séminaire Lotharingien de Combinatoire, vol. 30, Discrete Mathematics, to appear.
27. G. Rauzy, Mots infinis en arithmétique, in: M. Nivat, D. Perrin (Eds.), Automata on Infinite Words, Lecture Notes in Computer Science, vol. 192, Springer, Berlin, 1984, pp. 165-171.
28. P. Séébold, Fibonacci morphisms and Sturmian words, Theoret. Comput. Sci. 88 (1991) 365-384.
29. P. Séébold, On the conjugation of Standard morphisms, in: W. Penczek, A. Szalas (Eds.), Proc. 18st Internat. Symp. MFCS, Lecture Notes in Computer Science, vol. 1113, Springer, Berlin, 1996, pp. 506-516.
30. B.A. Venkov, Elementary Number Theory, Wolters-Noordhoff, Groningen, 1970.
31. Z.-X. Wen, Z.-Y Wen, Local isomorphisms of invertible substitutions, Comptes rendus de l'Académie des Sciences 318 (1994) 299-304.