s-convexity, model sets and their relation
Zuzana Masáková, Jiří Patera, Edita Pelantová
Abstract
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 12(1+5), 1+2, and 2+3 related to experimentally observed non-crystallographic symmetries are exceptional with respect to s-convexity.
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