A numeration system for Fibonacci-like Wang shifts and > its properties.
1 : Laboratoire Bordelais de Recherche en Informatique
Centre National de la Recherche Scientifique : UMR5800, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Université Sciences et Technologies - Bordeaux 1, Université Bordeaux Segalen - Bordeaux 2
Motivated by the study of Fibonacci-like Wang shifts,
we define a numeration system $\Fcal$ for $\mathbb{Z}$ and $\mathbb{Z}^2$
based on the binary alphabet $\{0,1\}$.
We introduce a set of 16 Wang tiles
that admits a valid tiling of the plane described by
a deterministic finite automaton
taking as input the representation of a position $(m,n)\in\mathbb{Z}^2$ in $\Fcal$ and
outputting a Wang tile. We show the properties of the numeration system $\Fcal$
with respect to addition, building on the work of Jean Berstel.
| Type : | : | oral 20min |
| Thématiques | : | SDA2 |
| PDF version | : |  PDF version |
