DOI : https://doi.org/10.5802/acirm.8
Keywords: Quasi-periodic tiling, Rauzy fractal, Stepped plane
@article{ACIRM_2009__1_1_41_0,
author = {Maki Furukado and Shunji Ito},
title = {Complex Pisot Numeration Systems},
journal = {Actes des rencontres du CIRM},
publisher = {CIRM},
volume = {1},
number = {1},
year = {2009},
pages = {41-48},
doi = {10.5802/acirm.8},
language = {en},
url = {https://acirm.centre-mersenne.org/item/ACIRM_2009__1_1_41_0}
}
Furukado, Maki; Ito, Shunji. Complex Pisot Numeration Systems. Actes des rencontres du CIRM, Volume 1 (2009) no. 1, pp. 41-48. doi : 10.5802/acirm.8. https://acirm.centre-mersenne.org/item/ACIRM_2009__1_1_41_0/
[A-F-H-I] P.Arnoux, M.Furukado, E.Harriss and S.Ito, Algebraic numbers and automorphisms of free groups, preprint. (2006).
[A-I] P.Arnoux and S.Ito, Pisot substitutions and Rauzy fractals, Journées Montoises d’Informatique Théorique (Marne-la-Vallée, 2000), Bull. Belg. Math. Soc. Simon Stevin 8 (2001), no. 2, 181–207.
[E-I] H.Ei and S.Ito Tiling from some non-irreducible Pisot substitutions, Discrete Math. Theor. Comput. Sci. 7 (2005), no. 1, 81–121.
[E] H.Ei, Some properties of invertible substitutions of rank d, and higher dimensional substitutions, Osaka J. Math. 40 (2003), 543–562.
[F-F-I-W] D.J.Feng, M.Furukado, S.Ito and J.Wu, Pisot substitutions and the Hausdorff dimension of boundaries of atomic surfaces, Tsukuba J. Math. 30, (2006), no. 1, 195-2235.
[F-I-R] M.Furukado, S.Ito and E.A.Robinson Jr., Tilings associated with non-Pisot matrices, Ann. Inst. Fourier, Grenoble 56, 7(2006) 2391-2435.
[F] M.Furukado Tilings from non-Pisot unimodular matrices, Hiroshima Math. J. 36 (2006), no. 2.
[H-F-I] M.Hama, M.Furukado and S.Ito, Complex Pisot Numeration Systems, to appear in Commentarii Mathematici Universitatis Sancti Pauli.
[I-R] S.Ito and H.Rao, Atomic surfaces, tilings and coincidence I. Irrecucible case, Israel J. Math. 153 (2006), 129-156.
[R] G. Rauzy, Nombres Algébriques et Substitutions, Bull. Soc. Math. France, 110 (1982), 147-178.