A self-similar tiling generated by the minimal Pisot number

Shigeki Akiyama; Taizo Sadahiro

Acta Mathematica et Informatica Universitatis Ostraviensis (1998)

  • Volume: 06, Issue: 1, page 9-26
  • ISSN: 1804-1388

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Akiyama, Shigeki, and Sadahiro, Taizo. "A self-similar tiling generated by the minimal Pisot number." Acta Mathematica et Informatica Universitatis Ostraviensis 06.1 (1998): 9-26. <http://eudml.org/doc/23814>.

@article{Akiyama1998,
author = {Akiyama, Shigeki, Sadahiro, Taizo},
journal = {Acta Mathematica et Informatica Universitatis Ostraviensis},
keywords = {fractal; plane tiling; Pisot number; beta-expansions},
language = {eng},
number = {1},
pages = {9-26},
publisher = {University of Ostrava},
title = {A self-similar tiling generated by the minimal Pisot number},
url = {http://eudml.org/doc/23814},
volume = {06},
year = {1998},
}

TY - JOUR
AU - Akiyama, Shigeki
AU - Sadahiro, Taizo
TI - A self-similar tiling generated by the minimal Pisot number
JO - Acta Mathematica et Informatica Universitatis Ostraviensis
PY - 1998
PB - University of Ostrava
VL - 06
IS - 1
SP - 9
EP - 26
LA - eng
KW - fractal; plane tiling; Pisot number; beta-expansions
UR - http://eudml.org/doc/23814
ER -

References

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  1. S. Akiyama, Pisot numbers and greedy algorithm, Number Theory, Diophantine, Computational and Algebraic Aspects, edited by K.Gyory, A. Petho and V.T. Sos, 9-21, de Gruyter, Berlin, New York (1998) (1998) Zbl0919.11063MR1628829
  2. M. J. Bertin A. Decomps-Guilloux M. Grandet-Hugot M. Pathiaux-Delefosse J. P. Schreiber, Pisot and Salem Numbers, Birkhauser Verlag Basel-Boston-Berlin. (1992) (1992) MR1187044
  3. K. J. Falconer, Techniques in Fractal Geometry, John Wiley & Sons.(1997) (1997) Zbl0869.28003MR1449135
  4. C. Frougny B. Solomyak, 10.1017/S0143385700007057, Ergod. Th. and Dynam. Sys. 12 (1992) 713-723 (1992) MR1200339DOI10.1017/S0143385700007057
  5. A. Messaoudi, Frontiere du fractal de Rauzy et systeme de numeration complexe, preprint. Zbl0968.28005MR1793161
  6. W. Parry, 10.1007/BF02020954, Acta Math. Acad. Sci. Hungar. 11 (1960) 269-278 (1960) Zbl0099.28103MR0142719DOI10.1007/BF02020954
  7. G. Rauzy, Nombres Algebriques et substitutions, Bull. Soc. France 110 (1982), 147-178. (1982) Zbl0522.10032MR0667748
  8. W. P. Thurston, Groups, Tilings and Finite state automata, Summer 1989 AMS Colloquium lectures, Research Report GCG 1. (1989) 

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