×
Berstel, J.; Séébold, P.

A remark on morphic Sturmian words. (English) Zbl 0883.68104

RAIRO, Inform. Théor. Appl. 28, No. 3-4, 255-263 (1994).
Summary: This note deals with binary Sturmian words that are morphic, i.e. generated by iterating a morphism. Among these, characteristic words are a well-known subclass. We prove that for every characteristic morphic word \(x\), the four words \(ax\), \(bx\), \(abx\) and \(bax\) are morphic.

Cited in 56 Documents

MSC:

68R15 Combinatorics on words
68Q45 Formal languages and automata

Keywords:

binary Sturmian words
PDF BibTeX XML Cite
\textit{J. Berstel} and \textit{P. Séébold}, RAIRO, Inform. Théor. Appl. 28, No. 3--4, 255--263 (1994; Zbl 0883.68104)
Full Text: DOI EuDML

References:

[1] 1. J. BERSTEL and P. SÉÉBOLD, A Characterization of Sturmian Morphisms, in: A. BORZYSKOWSKI, S. SOKOLOWSKI (eds.) MFCS’93, Leci. Notes Comp. Sci., 1993, 711, pp. 281-290. Zbl0925.11026 MR1265070 · Zbl 0925.11026
[2] 2. E. BOMBIERI and J. E. TAYLOR, Which Distributions of Matter DiffractW? An Initial Investigation, J. Phys., 1986, 47, Colloque C3, pp. 19-28. Zbl0693.52002 MR866320 · Zbl 0693.52002
[3] 3. J.-P. BOREL and F. LAUBIE, Quelques mots sur la droite projective réelle, J. théorie des nombres de Bordeaux, 1993, 5, pp. 23-52. Zbl0839.11008 MR1251226 · Zbl 0839.11008
[4] 4. T. C. BROWN, Descriptions of the Characteristic Sequence of an Irrational, Canad. Math. Bull., 1993, 36, 1, pp. 15-21. Zbl0804.11021 MR1205889 · Zbl 0804.11021
[5] 5. E. COVEN and G. HEDLUND, Sequences with Minimal Block Growth, Math. Systems Theory, 1973, 7, pp.138-153. Zbl0256.54028 MR322838 · Zbl 0256.54028
[6] 6. D. CRISP, W. MORAN, A. POLLINGTON, P. SHIUE, Subsitution Invariant Cutting Sequences, J. théorie des nombres de Bordeaux, 1993, 5, pp. 123-138. Zbl0786.11041 MR1251232 · Zbl 0786.11041
[7] 7. K. CULIK II and S. DUBE, Rational and Affine Expressions for Image Descriptions, Discrete Appl. Math., 1993, 41, pp. 85-120. Zbl0784.68058 MR1198549 · Zbl 0784.68058
[8] 8. K. CULIK II and S. DUBE, L-Systems and Mutually Recursive Function Systems, Acta Inform., 1993, 30, pp. 279-302. Zbl0790.68056 MR1227886 · Zbl 0790.68056
[9] 9. K. CULIK II and S. DUBE, Encoding Images as Words and Languages, Intern. J. Algebra Comput., 1993, 3, pp. 221-236. Zbl0777.68056 MR1233222 · Zbl 0777.68056
[10] 10. K. CULIK II and T. HARJU, Dominoes, Slicing Semigroups and DNA, Discrete Appl. Math., 1991, 31, pp. 261-277. Zbl0747.20035 MR1110460 · Zbl 0747.20035
[11] 11. K. CULIK II and J. KARHUMÄKI, Iterative Devices Generating Infinite Words, Intern. J. Algebra Comput. (to appear). · Zbl 0900.68337
[12] 12. K. CULIK II and J. KARI, Image Compression Using Weighted Automata, Computer and Graphics, 1993, 17, pp. 305-313. · Zbl 0813.68159
[13] 13. K. CULIK II and A. SALOMAA, On Infinite Words Obtained by Iterating Morphisms, Theoret. Comput. Sci., 1982, 19, pp. 29-38. Zbl0492.68059 MR664411 · Zbl 0492.68059
[14] 14. A. DE LUCA and F. MIGNOSI, Some Combinatorial Properties of Sturmian Words, Theoret. Comput. Sci. (to appear). Also Available as Technical Report LITP 93-53, october 1993. Zbl0874.68245 MR1872447 · Zbl 0874.68245
[15] 15. G. HEDGLUND and M. MORSE, Symbolic Dynamics II: Sturmian Sequences, Amer. J. Math., 1940, 61, pp. 1-42. JFM66.0188.03 · JFM 66.0188.03
[16] 16. F. MIGNOSI, P. SÉÉBOLD, Morphismes sturmiens et règles de Rauzy, J. théorie des nombres de Bordeaux, 1993, 5, pp. 221-233. Zbl0797.11029 MR1265903 · Zbl 0797.11029
[17] 17. A. SALOMAA, Morphisms on Free Monoids and Language Theory, in Formal Language Theory: Perspectives and Open Problems, 1980, pp. 141-166, Academic Press.
[18] 18. A. SALOMAA, Jewels of Formal Language Theory, Computer Science Press, 1981. Zbl0487.68064 MR618124 · Zbl 0487.68064
[19] 19. Z.-X. WEN and Z.-Y. WEN, Local Isomorphisms of Invertible Substitutions, C. R. Acad. Sci. Paris (to appear). Zbl0812.11018 · Zbl 0812.11018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.