s-convexity, model sets and their relation

Edita Pelantov\'a; Ji\v{r}\'i Patera; Zuzana Mas\'akov\'a

arxiv: math/9907054 · v1 · pith:CIDWDJ4Bnew · submitted 1999-07-08 · 🧮 math.RA · math-ph· math.MP· math.NT

s-convexity, model sets and their relation

Zuzana Mas\'akov\'a , Ji\v{r}\'i Patera , Edita Pelantov\'a This is my paper

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keywords s-convexitysetsmodelnumberspisotquasicrystalsrelatedrelation

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The relation of s-convexity and sets modeling physical quasicrystals is explained for quasicrystals related to quadratic unitary Pisot numbers. We show that 1-dimensional model sets may be characterized by s-convexity for finite set of parameters s. It is shown that the three Pisot numbers $\frac12(1+\sqrt5)$, $1+\sqrt2$, and $2+\sqrt3$ related to experimentally observed non-crystallographic symmetries are exceptional with respect to s-convexity.

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s-convexity, model sets and their relation

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