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- W2078250711 abstract "We consider one-dimensional aperiodic sequences arising from a cut-and-project scheme with quadratic unitary Pisot numbers β. A construction of the substitution rule is described under rather general assumptions. It allows one to build a given cut-and-project sequence Σβ(Ω) starting from its arbitrary point. For a sequence with a convex acceptance window interval Ω, we prove that a substitution rule exists precisely if the boundary points of Ω are in the corresponding quadratic field [β]. Typically such a substitution has a reducible characteristic polynomial. Our main result is an algorithm for construction of such a substitution rule. Some examples are shown." @default.
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- W2078250711 date "2000-11-24" @default.
- W2078250711 modified "2023-09-30" @default.
- W2078250711 title "Substitution rules for aperiodic sequences of the cut and project type" @default.
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- W2078250711 doi "https://doi.org/10.1088/0305-4470/33/48/319" @default.
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