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Complex Pisot Numeration Systems
Maki Furukado1; Shunji Ito2
1 Yokohama
2 Kanazawa
Actes des rencontres du CIRM, Volume 1 (2009) no. 1, pp. 41-48.
Published online:
DOI: 10.5802/acirm.8
Keywords: Quasi-periodic tiling, Rauzy fractal, Stepped plane
Maki Furukado 1; Shunji Ito 2

1 Yokohama
2 Kanazawa 
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Maki Furukado; Shunji Ito. 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/articles/10.5802/acirm.8/

[A-F-H-I] P.Arnoux, M.Furukado, E.Harriss and S.Ito, Algebraic numbers and automorphisms of free groups, preprint. (2006). | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[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. | Zbl

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

[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. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[F] M.Furukado Tilings from non-Pisot unimodular matrices, Hiroshima Math. J. 36 (2006), no. 2. | DOI | MR | Zbl

[H-F-I] M.Hama, M.Furukado and S.Ito, Complex Pisot Numeration Systems, to appear in Commentarii Mathematici Universitatis Sancti Pauli. | DOI | MR | Zbl

[I-R] S.Ito and H.Rao, Atomic surfaces, tilings and coincidence I. Irrecucible case, Israel J. Math. 153 (2006), 129-156. | DOI | MR

[R] G. Rauzy, Nombres Algébriques et Substitutions, Bull. Soc. Math. France, 110 (1982), 147-178. | DOI | Zbl

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