A generalization of Sturmian sequences: Combinatorial structure and transcendence

Rebecca Risley; Luca Zamboni

Acta Arithmetica (2000)

  • Volume: 95, Issue: 2, page 167-184
  • ISSN: 0065-1036

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Risley, Rebecca, and Zamboni, Luca. "A generalization of Sturmian sequences: Combinatorial structure and transcendence." Acta Arithmetica 95.2 (2000): 167-184. <http://eudml.org/doc/207445>.

@article{Risley2000,
author = {Risley, Rebecca, Zamboni, Luca},
journal = {Acta Arithmetica},
keywords = {uniformly recurrent sequences; alphabet; Sturmian sequences; Arnoux-Rauzy sequences; combinatorial algorithm; bispecial words; primitive morphic Arnoux-Rauzy sequences; transcendental numbers},
language = {eng},
number = {2},
pages = {167-184},
title = {A generalization of Sturmian sequences: Combinatorial structure and transcendence},
url = {http://eudml.org/doc/207445},
volume = {95},
year = {2000},
}

TY - JOUR
AU - Risley, Rebecca
AU - Zamboni, Luca
TI - A generalization of Sturmian sequences: Combinatorial structure and transcendence
JO - Acta Arithmetica
PY - 2000
VL - 95
IS - 2
SP - 167
EP - 184
LA - eng
KW - uniformly recurrent sequences; alphabet; Sturmian sequences; Arnoux-Rauzy sequences; combinatorial algorithm; bispecial words; primitive morphic Arnoux-Rauzy sequences; transcendental numbers
UR - http://eudml.org/doc/207445
ER -

References

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  1. [1] J.-P. Allouche and L. Q. Zamboni, Algebraic irrational binary numbers cannot be fixed points of non-trivial constant length or primitive morphisms, J. Number Theory 69 (1998), 119-124. Zbl0918.11016
  2. [2] P. Arnoux and S. Ito, Pisot substitutions and Rauzy fractals, preprint, 1999. Zbl1007.37001
  3. [3] P. Arnoux et G. Rauzy, Représentation géométrique de suites de complexité 2 n + 1 , Bull. Soc. Math. France 119 (1991), 199-215. Zbl0789.28011
  4. [4] J. Berstel, Mots de Fibonacci, Séminaire d'Informatique Théorique, LITP, Universités Paris 6-7 (1980-1981), 57-78. 
  5. [5] J. Berstel et P. Séébold, Morphismes de Sturm, Bull. Belg. Math. Soc. 1 (1994), 175-189. 
  6. [6] V. Berthé, Fréquences des facteurs des suites sturmiennes, Theoret. Comput. Sci. 165 (1996), 295-309. 
  7. [7] M. G. Castelli, F. Mignosi and A. Restivo, Fine and Wilf's theorem for three periods and a generalization of sturmian words, ibid. 218 (1999), 83-94. Zbl0916.68114
  8. [8] N. Chekhova, Les suites d'Arnoux-Rauzy : algorithme d'approximation et propriétés ergodiques, preprint, 1998. 
  9. [9] N. Chekhova, P. Hubert et A. Messaoudi, Propriétés combinatoires, ergodiques et arithmétiques de la substitution de Tribonacci, J. Théor. Nombres Bordeaux, to appear. 
  10. [10] E. M. Coven and G. A. Hedlund, Sequences with minimal block growth, Math. Systems Theory 7 (1973), 138-153. Zbl0256.54028
  11. [11] A. de Luca and F. Mignosi, Some combinatorial properties of Sturmian words, Theoret. Comput. Sci. 136 (1994), 361-385. Zbl0874.68245
  12. [12] F. Durand, A characterization of substitutive sequences using return words, Discrete Math. 179 (1998), 89-101. Zbl0895.68087
  13. [13] F. Durand, Linearly recurrent subshifts, Ergod. Theory Dynam. Systems, to appear. 
  14. [14] F. Durand and B. Host, private communication. 
  15. [15] F. Durand, B. Host and C. Skau, Substitution dynamical systems, Bratteli diagrams and dimension groups, Ergod. Theory Dynam. Systems 19 (1999), 953-993. Zbl1044.46543
  16. [16] S. Ferenczi, Les transformations de Chacon : combinatoire, structure géométrique, lien avec les systèmes de complexité 2 n + 1 , Bull. Soc. Math. France 123 (1995), 271-292. 
  17. [17] S. Ferenczi and C. Mauduit, Transcendence of numbers with a low complexity expansion, J. Number Theory 67 (1997), 146-161. Zbl0895.11029
  18. [18] C. Holton and L. Q. Zamboni, Descendants of primitive substitutions, Theory Comput. Syst. 32 (1998), 133-157. Zbl0916.68086
  19. [19] C. Holton and L. Q. Zamboni, Directed graphs and substitutions, in: From Crystals to Chaos, P. Hubert, R. Lima and S. Vaienti (eds.), World Sci., 1999, to appear. 
  20. [20] J. H. Loxton and A. van der Poorten, Arithmetic properties of automata: regular sequences, J. Reine Angew. Math. 392 (1988), 57-69. 
  21. [21] K. Mahler, Lectures on Diophantine Approximations, Part I: g -adic Numbers and Roth’s Theorem, Univ. of Notre Dame, 1961. Zbl0158.29903
  22. [22] K. Mahler, Arithmetische Eigenschaften einer Klasse von Dezimalbrüchen, Proc. Konink. Nederl. Akad. Wetensch. Ser. A 40 (1937), 421-428. Zbl0017.05602
  23. [23] F. Mignosi, Infinite words with linear subword complexity, Theoret. Comput. Sci. 65 (1989), 221-242. Zbl0682.68083
  24. [24] F. Mignosi, On the number of factors of Sturmian words, ibid. 82 (1991), 71-84. Zbl0728.68093
  25. [25] F. Mignosi and G. Pirillo, Repetitions in the Fibonacci infinite word, RAIRO Inform. Théor. Appl. 26 (1992), 199-204. Zbl0761.68078
  26. [26] M. Morse and G. A. Hedlund, Symbolic dynamics, Amer. J. Math. 60 (1938), 815-866. Zbl0019.33502
  27. [27] M. Morse and G. A. Hedlund, Symbolic dynamics II: Sturmian sequences, ibid. 62 (1940), 1-42. Zbl0022.34003
  28. [28] M. Queffélec, Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Math. 1294, Springer, 1987. 
  29. [29] G. Rauzy, Mots infinis en arithmétique, in: Automata on Infinite Words, M. Nivat and D. Perrin (eds.), Lecture Notes in Comput. Sci. 192, Springer, Berlin, 1985, 165-171. Zbl0613.10044
  30. [30] G. Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France 110 (1982), 147-178. Zbl0522.10032
  31. [31] G. Rote, Sequences with subword complexity 2 n , J. Number Theory 46 (1994), 196-213. Zbl0804.11023
  32. [32] J.-I. Tamura, A class of transcendental numbers having explicit g -adic and Jacobi-Perron expansions of arbitrary dimension, Acta Arith. 71 (1995), 301-329. Zbl0828.11036
  33. [33] N. Wozny and L. Q. Zamboni, Frequencies of factors in Arnoux-Rauzy sequences, Acta Arith., to appear. Zbl0973.11030
  34. [34] L. Q. Zamboni, Une généralisation du théorème de Lagrange sur le développement en fraction continue, C. R. Acad. Sci. Paris Sér. I, 327 (1998), 527-530. 

Citations in EuDML Documents

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  1. Antonio Restivo, Giovanna Rosone, On the product of balanced sequences
  2. Tomi Kärki, Transcendence of numbers with an expansion in a subclass of complexity 2 + 1
  3. Antonio Restivo, Giovanna Rosone, On the product of balanced sequences
  4. Filippo Mignosi, Luca Q. Zamboni, A note on a conjecture of Duval and sturmian words
  5. Filippo Mignosi, Luca Q. Zamboni, A Note on a Conjecture of Duval and Sturmian Words
  6. Jacques Justin, Giuseppe Pirillo, On a characteristic property of Arnoux–Rauzy sequences
  7. Jacques Justin, Giuseppe Pirillo, On a characteristic property of ARNOUX–RAUZY sequences
  8. Amy Glen, Florence Levé, Gwénaël Richomme, Directive words of episturmian words : equivalences and normalization
  9. Jacques Justin, Episturmian morphisms and a Galois theorem on continued fractions
  10. Amy Glen, Florence Levé, Gwénaël Richomme, Directive words of episturmian words: equivalences and normalization

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