Regular subdivision in \(\mathbb{Z} [\frac{1+\sqrt{5}}{2}]\)
The author shows how to construct ``regular'' subdivisions for the ring \(\mathbb{Z}[ \frac{1+\sqrt{5}}{2} ]\). He relates these subdivisions to the Fibonacci tiling and to the two substitutions \(L\to LS\), \(S\to L\) and \(L\to SL\), \(S\to L\) (used inter alia to produce one-dimensional quasi-crystals in the literature in physics). A more general result for general algebraic rings is announced.
scientific article; zbMATH DE number 1525072