English

s-convexity, model sets and their relation

Rings and Algebras 2016-08-15 v1 Mathematical Physics math.MP Number Theory

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)\frac12(1+\sqrt5), 1+21+\sqrt2, and 2+32+\sqrt3 related to experimentally observed non-crystallographic symmetries are exceptional with respect to s-convexity.

Keywords

Cite

@article{arxiv.math/9907054,
  title  = {s-convexity, model sets and their relation},
  author = {Zuzana Masáková and Jiří Patera and Edita Pelantová},
  journal= {arXiv preprint arXiv:math/9907054},
  year   = {2016}
}