Tilings of a Riemann surface and cubic Pisot numbers
Enomoto, Fumihiko ; Ei, Hiromi ; Furukado, Maki ; Ito, Shunji
Hiroshima Math. J., Tome 37 (2007) no. 1, p. 181-210 / Harvested from Project Euclid
Using the reducible algebraic polynomial \(x^{5} - x^{4}-1 = \left( x^{2}-x + 1 \right) \left( x^{3} - x - 1 \right),\) we study two types of tiling substitutions $\tau^*$ and $\sigma^*$: $\tau^*$ generates a tiling of a plane based on five prototiles of polygons, and $\sigma^*$ generates a tiling of a Riemann surface, which consists of two copies of the plane, based on ten prototiles of parallelograms. Finally we claim that $\tau^*$-tiling of $\mathcal{P}$ equals a re-tiling of $\sigma^*$-tiling of $\mathcal{R}$ through the canonical projection of the Riemann surface to the plane.
Publié le : 2007-07-14
Classification:  Quasi-periodic tiling of a Riemann surface,  tiling substitution generated by a reducible cubic Pisot number,  52C23,  37A45,  28A80
@article{1187916318,
     author = {Enomoto, Fumihiko and Ei, Hiromi and Furukado, Maki and Ito, Shunji},
     title = {Tilings of a Riemann surface and cubic Pisot numbers},
     journal = {Hiroshima Math. J.},
     volume = {37},
     number = {1},
     year = {2007},
     pages = { 181-210},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1187916318}
}
Enomoto, Fumihiko; Ei, Hiromi; Furukado, Maki; Ito, Shunji. Tilings of a Riemann surface and cubic Pisot numbers. Hiroshima Math. J., Tome 37 (2007) no. 1, pp.  181-210. http://gdmltest.u-ga.fr/item/1187916318/