Discrete geometry and numeration

Valérie Berthé

Actes des rencontres du CIRM (2009)

  • Volume: 1, Issue: 1, page 17-22
  • ISSN: 2105-0597

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Berthé, Valérie. "Discrete geometry and numeration." Actes des rencontres du CIRM 1.1 (2009): 17-22. <http://eudml.org/doc/10003>.

@article{Berthé2009,
author = {Berthé, Valérie},
journal = {Actes des rencontres du CIRM},
keywords = {discrete geometry; combinatorics; Sturmian words; dynamic systems; stepped surface; Tribonacci substitution; Rauzy fractal},
language = {eng},
month = {3},
number = {1},
pages = {17-22},
publisher = {CIRM},
title = {Discrete geometry and numeration},
url = {http://eudml.org/doc/10003},
volume = {1},
year = {2009},
}

TY - JOUR
AU - Berthé, Valérie
TI - Discrete geometry and numeration
JO - Actes des rencontres du CIRM
DA - 2009/3//
PB - CIRM
VL - 1
IS - 1
SP - 17
EP - 22
LA - eng
KW - discrete geometry; combinatorics; Sturmian words; dynamic systems; stepped surface; Tribonacci substitution; Rauzy fractal
UR - http://eudml.org/doc/10003
ER -

References

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  2. P. Arnoux, V. Berthé, S. Ito, Discrete planes, ℤ 2 -actions, Jacobi-Perron algorithm and substitutions, Ann. Inst. Fourier (Grenoble) 52 (2002), 1001–1045. Zbl1017.11006MR1906478
  3. V. Berthé, Th. Fernique, Brun expansions of stepped surfaces, preprint. Zbl1236.11011
  4. V. Berthé, A. Siegel, Tilings associated with beta-numeration and substitutions, Integers: electronic journal of combinatorial number theory 5 (2005), A02. Zbl1139.37008MR2191748
  5. V. Berthé, C. Holton, L.Q. Zamboni, Initial powers of Sturmian words, Acta Arithmetica 122 (2006), 315–347. Zbl1117.37005MR2234421
  6. A. J. Brentjes, Multi-dimensional continued fraction algorithms, Mathematical Centre Tracts 145, Matematisch Centrum, Amsterdam, 1981. Zbl0471.10024MR638474
  7. H. Ei, Some properties of invertible substitutions of rank d and higher dimensional substitutions, Osaka J. Math. 40 (2003), 543–562. Zbl1037.20033MR1988704
  8. Th. Fernique, Multi-dimensional Sequences and Generalized Substitutions, Int. J. Fond. Comput. Sci. 17 (2006), 575–600. Zbl1096.68125MR2234803
  9. Th. Fernique, Generation and recognition of digital planes using multi-dimensional continued fractions, to appear in Pattern Recognition, http://www.lif.univ-mrs.fr/~fernique/. Zbl1138.68592MR2503454
  10. S. Ito, M. Ohtsuki, Modified Jacobi-Perron algorithm and generating Markov partitions for special hyperbolic toral automorphisms, Tokyo J. Math. 16, (1993), 441–472. Zbl0805.11056MR1247666
  11. D. Jamet, J.-L. Toutant Minimal arithmetic thickness connecting discrete planes, Discrete Applied Mathematics 157 (2009), 500–509. Zbl1169.68050MR2479142
  12. J. C. Lagarias, Geodesic multidimensional continued fractions, Proc. London Math. Soc. 69 (1994), 464–488. Zbl0813.11040MR1289860
  13. N. Lothaire, Algebraic combinatorics on words, Cambridge University Press, 2002. Zbl1001.68093MR1905123
  14. N. Pytheas Fogg, Substitutions in Dynamics, Arithmetics, and Combinatorics, Lecture Notes in Mathematics 1794, Springer Verlag. V. Berthé, S. Ferenczi, C. Mauduit and A. Siegel, Eds. (2002). Zbl1014.11015MR1970385
  15. M. Queffélec, Substitution dynamical systems–spectral analysis, Lecture Notes in Mathematics 1294 (1987). Zbl0642.28013MR924156
  16. J.-P. Réveilles, Calcul en nombres entiers et algorithmique, Thèse d’État, Univ. Louis Pasteur, Strasbourg (1991). 
  17. F. Schweiger, Multi-dimensional continued fractions, Oxford Science Publications, Oxford Univ. Press, Oxford (2000). Zbl0981.11029
  18. N. Sidorov, Arithmetic dynamics, Topics in dynamics and ergodic theory, Lond. Math. Soc. Lect. Note Ser. 310 (2003), 145–189. Cambridge Univ. Press. Zbl1051.37007MR2052279
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