Repetitions in Sturmian strings

Theoretical Computer Science

Volumn 249, Issue 2, 2000, Pages 289-303

  Franěk, František ^a   Karaman, Ayşe ^a   Smyth, W F ^a,b  

^a MCMASTER UNIVERSITY   (Canada)

^b CURTIN UNIVERSITY   (Australia)

Author keywords

Algorithm; Repetition; String; Sturmian; Word

Indexed keywords

EID: 0347899637     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(00)00063-3     Document Type: Article

References (15)

1. J. Berstel, Recent results in sturmian words, Developments in Language Theory, World Scientific, Singapore (1996) 13-24.
2. J. Berstel, P. Séébold, A characterization of Sturmian morphisms, in: A. Borzyszkowski & S. Sokolowski (Ed.), The Mathematical Foundations of Computer Science, Springer, Berlin, 1993, pp. 281-290.
3. E.B. Christoffel, Observatio Arithmetica, Ann. Math. Pura Appl. 6 (1875) 145-152.
4. M. Crochemore, An optimal algorithm for computing all the repetitions in a word, Inform. Process. Lett. 12-5 (1981) 244-248.
5. S. Dulucq, D. Gouyou-Beauchamps, Sur les facteurs des suites de Sturm, Theoret. Comput. Sci. 71 (1990) 381-400.
6. C.S. Iliopoulos, W.F. Smyth, A characterization of the squares in a Fibonacci string, Theoret. Comput. Sci. 172 (1997) 281-291.
7. A. Karaman, W.F. Smyth, A Representation of Sturmian Strings, Tech. Rep. No. CAS 98-04, Department of Computing & Software, McMaster University (1998): http://www.cas.mcmaster.ca/cas/research/ reports.html.
8. A. Luca, F. Mignosi, Some combinatorial properties of Sturmian words, Theoret. Comput. Sci. 136 (1994) 361-385.
9. W.F. Lunnon, P.A.B. Pleasants, Characterization of two-distance sequences, J. Austral. Math. Soc. Ser. A 53 (1992) 198-218.
10. F. Mignosi, On the number of factors of Sturmian words, Theoret. Comput. Sci. 82 (1989) 221-242.
11. F. Mignosi, P. Séébold, Morphismes sturmiens et règles de Rauzy, J. Théorie des Nombres de Bordeaux 5 (1993) 221-233.
12. M. Morse, G.A. Hedlund, Symbolic dynamics II: Sturmian trajectories, Amer. J. Math. 62 (1940) 1-42.
13. 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.
14. K.B. Stolarsky, Beatty sequences, continued fractions and certain shift operators, Canad. Math. Bull. 19-4 (1976) 473-481.
15. A. Thue, Über unendliche zeichenreihen, Norske Vid. Selsk. Skr. I, Mat. Nat. Kl. Christiana 7 (1906) 1-22.