no. 1
Discrete geometry and numeration
Actes des rencontres du CIRM, Tome 1 (2009) no. 1, pp. 17-22.
Publié le :
DOI : 10.5802/acirm.4 
@article{ACIRM_2009__1_1_17_0,
     author = {Berth\'e, Val\'erie},
     title = {Discrete geometry and numeration},
     journal = {Actes des rencontres du CIRM},
     pages = {17--22},
     publisher = {CIRM},
     volume = {1},
     number = {1},
     year = {2009},
     doi = {10.5802/acirm.4},
     zbl = {06938552},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/acirm.4/}
}
TY  - JOUR
AU  - Berthé, Valérie
TI  - Discrete geometry and numeration
JO  - Actes des rencontres du CIRM
PY  - 2009
SP  - 17
EP  - 22
VL  - 1
IS  - 1
PB  - CIRM
UR  - http://www.numdam.org/articles/10.5802/acirm.4/
DO  - 10.5802/acirm.4
LA  - en
ID  - ACIRM_2009__1_1_17_0
ER  - 
%0 Journal Article
%A Berthé, Valérie
%T Discrete geometry and numeration
%J Actes des rencontres du CIRM
%D 2009
%P 17-22
%V 1
%N 1
%I CIRM
%U http://www.numdam.org/articles/10.5802/acirm.4/
%R 10.5802/acirm.4
%G en
%F ACIRM_2009__1_1_17_0
Berthé, Valérie. Discrete geometry and numeration. Actes des rencontres du CIRM, Tome 1 (2009) no. 1, pp. 17-22. doi : 10.5802/acirm.4. http://www.numdam.org/articles/10.5802/acirm.4/

[1] P. Arnoux, S. Ito, Pisot substitutions and Rauzy fractals, Bull. Bel. Math. Soc. Simon Stevin 8 (2001), 181–207. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[3] V. Berthé, Th. Fernique, Brun expansions of stepped surfaces, preprint. | DOI | MR | Zbl

[4] V. Berthé, A. Siegel, Tilings associated with beta-numeration and substitutions, Integers: electronic journal of combinatorial number theory 5 (2005), A02. | Zbl

[5] V. Berthé, C. Holton, L.Q. Zamboni, Initial powers of Sturmian words, Acta Arithmetica 122 (2006), 315–347. | DOI | MR | Zbl

[6] A. J. Brentjes, Multi-dimensional continued fraction algorithms, Mathematical Centre Tracts 145, Matematisch Centrum, Amsterdam, 1981. | Zbl

[7] H. Ei, Some properties of invertible substitutions of rank d and higher dimensional substitutions, Osaka J. Math. 40 (2003), 543–562. | Zbl

[8] Th. Fernique, Multi-dimensional Sequences and Generalized Substitutions, Int. J. Fond. Comput. Sci. 17 (2006), 575–600. | DOI | MR

[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/. | DOI | Zbl

[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. | DOI | MR | Zbl

[11] D. Jamet, J.-L. Toutant Minimal arithmetic thickness connecting discrete planes, Discrete Applied Mathematics 157 (2009), 500–509. | DOI | MR | Zbl

[12] J. C. Lagarias, Geodesic multidimensional continued fractions, Proc. London Math. Soc. 69 (1994), 464–488. | DOI | MR | Zbl

[13] N. Lothaire, Algebraic combinatorics on words, Cambridge University Press, 2002. | DOI | Zbl

[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). | DOI | Zbl

[15] M. Queffélec, Substitution dynamical systems–spectral analysis, Lecture Notes in Mathematics 1294 (1987). | DOI | Zbl

[16] J.-P. Réveilles, Calcul en nombres entiers et algorithmique, Thèse d’État, Univ. Louis Pasteur, Strasbourg (1991). | Zbl

[17] F. Schweiger, Multi-dimensional continued fractions, Oxford Science Publications, Oxford Univ. Press, Oxford (2000). | Zbl

[18] N. Sidorov, Arithmetic dynamics, Topics in dynamics and ergodic theory, Lond. Math. Soc. Lect. Note Ser. 310 (2003), 145–189. Cambridge Univ. Press. | DOI | Zbl

[19] A. M. Vershik and A. N. Livshits, Adic models of ergodic transformations, spectral theory, substitutions, and related topics, Representation theory and dynamical systems (1992) 185–204. Amer. Math. Soc., Providence, RI. | DOI | Zbl

Cité par Sources :