Quelques mots sur la droite projective réelle

J.-P. Borel; F. Laubie

Journal de théorie des nombres de Bordeaux (1993)

  • Volume: 5, Issue: 1, page 23-51
  • ISSN: 1246-7405

How to cite

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Borel, J.-P., and Laubie, F.. "Quelques mots sur la droite projective réelle." Journal de théorie des nombres de Bordeaux 5.1 (1993): 23-51. <http://eudml.org/doc/93576>.

@article{Borel1993,
author = {Borel, J.-P., Laubie, F.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {combinatorics on words; Lyndon word; homography; substitutions; infinite Christoffel words},
language = {fre},
number = {1},
pages = {23-51},
publisher = {Université Bordeaux I},
title = {Quelques mots sur la droite projective réelle},
url = {http://eudml.org/doc/93576},
volume = {5},
year = {1993},
}

TY - JOUR
AU - Borel, J.-P.
AU - Laubie, F.
TI - Quelques mots sur la droite projective réelle
JO - Journal de théorie des nombres de Bordeaux
PY - 1993
PB - Université Bordeaux I
VL - 5
IS - 1
SP - 23
EP - 51
LA - fre
KW - combinatorics on words; Lyndon word; homography; substitutions; infinite Christoffel words
UR - http://eudml.org/doc/93576
ER -

References

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  1. [1] J. Bernoulli, Recueil pour les astronomes, Berlin, 1772. 
  2. [2] J. Berstel, Fibonacci words - a survey, in G. Rozenberg, A. Salomaa, ed., the Book of L, Springer Verlag (1986), 13-27. Zbl0589.68053
  3. [3] J.-P. Borel, F. Laubie, Construction de mots de Christoffel, C. R. Acad. Sci. Paris, Série I313 (1991), 483-485. Zbl0742.11013MR1131859
  4. [4] T.C. Brown, A characterisation of the quadratic irrationals, Canad. Math. Bull.34 (1991), 36-41. Zbl0688.10007MR1108926
  5. [5] T.C. Brown, Descriptions of the characteristic sequence of an irrational, Canad. Math. Bull.36 (1993), 15-21. Zbl0804.11021MR1205889
  6. [6] D. Crisp, W. Moran, A. Pollington, P. Shiue, Substitution invariant cutting sequences, Séminaire de Théorie des Nombres de Bordeaux, Série II, ce volume. Zbl0786.11041
  7. [7] E.B. Christoffel, Observatio arithmetica, Annali di Matematica, Ser. 26 (1875), 145-152. JFM06.0113.02
  8. [8] G.H. Hardy, E.M. Wright, An introduction to the theory of numbers, Oxford at the Clarendom Press, 4th ed., 1960. Zbl0086.25803MR568909
  9. [9] S. Ito, S. Yasutomi, On continued fractions, substitutions and characteristic sequences [nx + y] - [(n - 1 )x + y], Japan J. Math.16 (1990), 287-306. Zbl0721.11009MR1091163
  10. [10] F. Laubie, Prolongements homographiques des substitutions de mots de Christoffel, C. R. Acad. Sci. Paris313 Série I (1991), 565-567. Zbl0768.11024MR1133485
  11. [11] K. Nishioka, I. Shiokawa, J. Tamura, Arithmetical properties of a certain power series, J. Number Theory42 (1992), 61-87. Zbl0770.11039MR1176421
  12. [12] D. Perrin, Factorization of Free Monoids, in M. Lothaire, Combinatorics on words, Encyclopedia of Math. and its Applications17, 63-99, Addison-Wesley, 1983. 
  13. [13] G.N. Raney, On Continued Fractions and Finite Automata, Math. Ann.206 (1973), 265-283. Zbl0251.10024MR340166
  14. [14] G. Rauzy, Mots infinis en arithmétique, in M. Nivat et D. Perrin ed., Automata on infinite words, Lecture Notes inComputer Science192 (1985), 165-171. Zbl0613.10044MR814741
  15. [15] J. Riss, Communication personnelle, 1974. 
  16. [16] G. Viennot, Algèbres de Lie libres et Monoïdes libres, Lecture Notes in Math.691 (1978). Zbl0395.17003MR516004

Citations in EuDML Documents

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  1. Alex Heinis, On low-complexity bi-infinite words and their factors
  2. J. Berstel, P. Séébold, A remark on morphic sturmian words
  3. Jean-Pierre Borel, Christophe Reutenauer, On Christoffel classes
  4. Jean-Pierre Borel, Christophe Reutenauer, On Christoffel classes
  5. Jacques Justin, Giuseppe Pirillo, On a characteristic property of ARNOUX–RAUZY sequences
  6. Jacques Justin, Giuseppe Pirillo, On a characteristic property of Arnoux–Rauzy sequences
  7. Éric Laurier, Opérations sur les mots de Christoffel
  8. Bruno Parvaix, Propriétés d'invariance des mots sturmiens
  9. Amy Glen, Jacques Justin, Episturmian words: a survey

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